/* solidosPlatonicos.cpp
*/
#include "solidosSuavizados.h"

void montaVetor1(void)
{
 int a=0;
 for (int j = 0; j <= 24; j++)
 {   
    iter_1[j][0] = v[0][a];//facej
    iter_1[j][1] = t[0][a];
    iter_1[j][2] = q[0][a];
    iter_1[j][3] = t[3][a];
    j++;

    iter_1[j][0] = t[0][a];//facej+1
    iter_1[j][1] = v[1][a];
    iter_1[j][2] = t[1][a];
    iter_1[j][3] = q[0][a];
    j++;

    iter_1[j][0] = q[0][a];//facej+2
    iter_1[j][1] = t[1][a];
    iter_1[j][2] = v[2][a];
    iter_1[j][3] = t[2][a];
    j++;

    iter_1[j][0] = t[3][a];//facej+3
    iter_1[j][1] = q[0][a];
    iter_1[j][2] = t[2][a];
    iter_1[j][3] = v[3][a];
    a++;
 }
 return;
}

void iteracao2(void)
{
 //pontos nas faces
 for (int j = 0; j <24; j++)
 {
    q_2[j] = (iter_1[j][0] + iter_1[j][1] + iter_1[j][2] + iter_1[j][3])/4;
 }

 //pontos nas linhas de intersecção
t_2[0][0] = (q_2[0]+q_2[23])/4 + (iter_1[0][0]+iter_1[0][1])/4; //face 1 (de 24)
t_2[1][0] = (q_2[0]+q_2[1])/4 + (iter_1[0][1]+iter_1[0][2])/4;
t_2[2][0] = (q_2[0]+q_2[3])/4 + (iter_1[0][2]+iter_1[0][3])/4;
t_2[3][0] = (q_2[0]+q_2[5])/4 + (iter_1[0][3]+iter_1[0][0])/4;

t_2[0][1] = (q_2[1]+q_2[22])/4 + (iter_1[1][0]+iter_1[1][1])/4; //face 2 (de 24)
t_2[1][1] = (q_2[1]+q_2[16])/4 + (iter_1[1][1]+iter_1[1][2])/4;
t_2[2][1] = (q_2[1]+q_2[2])/4 + (iter_1[1][2]+iter_1[1][3])/4;
t_2[3][1] = t_2[1][0];

t_2[0][2] = t_2[2][1]; //face 3 (de 24)
t_2[1][2] = (q_2[2]+q_2[19])/4 + (iter_1[2][1]+iter_1[2][2])/4;
t_2[2][2] = (q_2[2]+q_2[9])/4 + (iter_1[2][2]+iter_1[2][3])/4;
t_2[3][2] = (q_2[2]+q_2[3])/4 + (iter_1[2][3]+iter_1[2][0])/4;

t_2[0][3] = t_2[2][0]; //face 4 (de 24)
t_2[1][3] = t_2[3][2];
t_2[2][3] = (q_2[3]+q_2[8])/4 + (iter_1[3][2]+iter_1[3][3])/4;
t_2[3][3] = (q_2[3]+q_2[6])/4 + (iter_1[3][3]+iter_1[3][0])/4;

t_2[0][4] = (q_2[4]+q_2[20])/4 + (iter_1[4][0]+iter_1[4][1])/4; //face 5 (de 24)
t_2[1][4] = (q_2[4]+q_2[5])/4 + (iter_1[4][1]+iter_1[4][2])/4;
t_2[2][4] = (q_2[4]+q_2[7])/4 + (iter_1[4][2]+iter_1[4][3])/4;
t_2[3][4] = (q_2[4]+q_2[13])/4 + (iter_1[4][3]+iter_1[4][0])/4;

t_2[0][5] = (q_2[5]+q_2[23])/4 + (iter_1[5][0]+iter_1[5][1])/4; //face 6 (de 24)
t_2[1][5] = t_2[3][0];
t_2[2][5] = (q_2[5]+q_2[6])/4 + (iter_1[5][2]+iter_1[5][3])/4;
t_2[3][5] = t_2[1][4];

t_2[0][6] = t_2[2][5]; //face 7 (de 24)
t_2[1][6] = t_2[3][3];
t_2[2][6] = (q_2[6]+q_2[8])/4 + (iter_1[6][2]+iter_1[6][3])/4;
t_2[3][6] = (q_2[6]+q_2[7])/4 + (iter_1[6][3]+iter_1[6][0])/4;

t_2[0][7] = t_2[2][4]; //face 8 (de 24)
t_2[1][7] = t_2[3][6];
t_2[2][7] = (q_2[7]+q_2[11])/4 + (iter_1[7][2]+iter_1[7][3])/4;
t_2[3][7] = (q_2[7]+q_2[14])/4 + (iter_1[7][3]+iter_1[7][0])/4;

t_2[0][8] = t_2[2][3]; //face 9 (de 24)
t_2[1][8] = (q_2[8]+q_2[9])/4 + (iter_1[8][1]+iter_1[8][2])/4;
t_2[2][8] = (q_2[8]+q_2[11])/4 + (iter_1[8][2]+iter_1[8][3])/4;
t_2[3][8] = t_2[2][6];

t_2[0][9] = t_2[2][2]; //face 10 (de 24)
t_2[1][9] = (q_2[9]+q_2[19])/4 + (iter_1[9][1]+iter_1[9][2])/4;
t_2[2][9] = (q_2[9]+q_2[10])/4 + (iter_1[9][2]+iter_1[9][3])/4;
t_2[3][9] = t_2[1][8];

t_2[0][10] = t_2[2][9]; //face 11 (de 24)
t_2[1][10] = (q_2[10]+q_2[18])/4 + (iter_1[10][1]+iter_1[10][2])/4;
t_2[2][10] = (q_2[10]+q_2[15])/4 + (iter_1[10][2]+iter_1[10][3])/4;
t_2[3][10] = (q_2[10]+q_2[11])/4 + (iter_1[10][3]+iter_1[10][0])/4;

t_2[0][11] = t_2[2][8]; //face 12 (de 24)
t_2[1][11] = t_2[3][10];
t_2[2][11] = (q_2[11]+q_2[14])/4 + (iter_1[11][2]+iter_1[11][3])/4;
t_2[3][11] = t_2[2][7];

t_2[0][12] = (q_2[12]+q_2[21])/4 + (iter_1[12][0]+iter_1[12][1])/4; //face 13 (de 24)
t_2[1][12] = (q_2[12]+q_2[13])/4 + (iter_1[12][1]+iter_1[12][2])/4;
t_2[2][12] = (q_2[12]+q_2[15])/4 + (iter_1[12][2]+iter_1[12][3])/4;
t_2[3][12] = (q_2[12]+q_2[17])/4 + (iter_1[12][3]+iter_1[12][0])/4;

t_2[0][13] = (q_2[13]+q_2[20])/4 + (iter_1[13][0]+iter_1[13][1])/4; //face 14 (de 24)
t_2[1][13] = t_2[3][4];
t_2[2][13] = (q_2[13]+q_2[14])/4 + (iter_1[13][2]+iter_1[13][3])/4;
t_2[3][13] = t_2[1][12];

t_2[0][14] = t_2[2][13]; //face 15 (de 24)
t_2[1][14] = t_2[3][7];
t_2[2][14] = t_2[2][11];
t_2[3][14] = (q_2[14]+q_2[15])/4 + (iter_1[14][3]+iter_1[14][0])/4;

t_2[0][15] = t_2[2][12]; //face 16 (de 24)
t_2[1][15] = t_2[3][14];
t_2[2][15] = t_2[2][10];
t_2[3][15] = (q_2[15]+q_2[18])/4 + (iter_1[15][3]+iter_1[15][0])/4;

t_2[0][16] = (q_2[16]+q_2[22])/4 + (iter_1[16][0]+iter_1[16][1])/4; //face 17 (de 24)
t_2[1][16] = (q_2[16]+q_2[17])/4 + (iter_1[16][1]+iter_1[16][2])/4;
t_2[2][16] = (q_2[16]+q_2[19])/4 + (iter_1[16][2]+iter_1[16][3])/4;
t_2[3][16] = t_2[1][1];

t_2[0][17] = (q_2[17]+q_2[21])/4 + (iter_1[17][0]+iter_1[17][1])/4; //face 18 (de 24)
t_2[1][17] = t_2[3][12];
t_2[2][17] = (q_2[17]+q_2[18])/4 + (iter_1[17][2]+iter_1[17][3])/4;
t_2[3][17] = t_2[1][16];

t_2[0][18] = t_2[2][17]; //face 19 (de 24)
t_2[1][18] = t_2[3][15];
t_2[2][18] = t_2[1][10];
t_2[3][18] = (q_2[18]+q_2[19])/4 + (iter_1[18][3]+iter_1[18][0])/4;

t_2[0][19] = t_2[2][16]; //face 20 (de 24)
t_2[1][19] = t_2[3][18];
t_2[2][19] = t_2[1][9];
t_2[3][19] = t_2[1][2];

t_2[0][20] = t_2[0][13]; //face 21 (de 24)
t_2[1][20] = (q_2[20]+q_2[21])/4 + (iter_1[20][1]+iter_1[20][2])/4;
t_2[2][20] = (q_2[20]+q_2[23])/4 + (iter_1[20][2]+iter_1[20][3])/4;
t_2[3][20] = t_2[0][4];

t_2[0][21] = t_2[0][12]; //face 22 (de 24)
t_2[1][21] = t_2[0][17];
t_2[2][21] = (q_2[21]+q_2[22])/4 + (iter_1[21][2]+iter_1[21][3])/4;
t_2[3][21] = t_2[1][20];

t_2[0][22] = t_2[2][21]; //face 23 (de 24)
t_2[1][22] = t_2[0][16];
t_2[2][22] = t_2[0][1];
t_2[3][22] = (q_2[22]+q_2[23])/4 + (iter_1[22][3]+iter_1[22][0])/4;

t_2[0][23] = t_2[2][20]; //face 24 (de 24) 
t_2[1][23] = t_2[3][22];
t_2[2][23] = t_2[0][0];
t_2[3][23] = t_2[0][5];

 //pontos de vértice = Q/4+2R/n+S(n-3)/n
v_2[0][0] = iter_1[0][0]/4 + (q_2[0]+q_2[5] +q_2[23])/12 +        ((iter_1[0][0]+iter_1[0][1])/2+(iter_1[0][0]+iter_1[5][2])/2 +(iter_1[0][0]+iter_1[23][0])/2)/6; //face1
v_2[1][0] = iter_1[0][1]/4 + (q_2[0]+q_2[23]+q_2[22]+q_2[1])/16 + ((iter_1[0][1]+iter_1[0][2])/2+(iter_1[0][1]+iter_1[23][3])/2+(iter_1[0][1]+iter_1[22][0])/2+(iter_1[0][1]+iter_1[1][1])/2)/8;
v_2[2][0] = iter_1[0][2]/4 + (q_2[0]+q_2[1] +q_2[2]+q_2[3])/16 +  ((iter_1[0][2]+iter_1[0][3])/2+(iter_1[0][2]+iter_1[1][0])/2 +(iter_1[0][2]+iter_1[2][1])/2+(iter_1[0][2]+iter_1[3][2])/2)/8;
v_2[3][0] = iter_1[0][3]/4 + (q_2[0]+q_2[3] +q_2[6]+q_2[5])/16 +  ((iter_1[0][3]+iter_1[0][0])/2+(iter_1[0][3]+iter_1[3][1])/2 +(iter_1[0][3]+iter_1[6][2])/2+(iter_1[0][3]+iter_1[5][3])/2)/8;

v_2[0][1] = v_2[1][0]; 
v_2[1][1] = iter_1[1][1]/4 + (q_2[1]+q_2[22]+q_2[16])/12 +        ((iter_1[1][1]+iter_1[1][2])/2+(iter_1[1][1]+iter_1[22][3])/2+(iter_1[1][1]+iter_1[16][1])/2)/6;
v_2[2][1] = iter_1[1][2]/4 + (q_2[1]+q_2[16]+q_2[19]+q_2[2])/16 + ((iter_1[1][2]+iter_1[1][3])/2+(iter_1[1][2]+iter_1[16][0])/2+(iter_1[2][1]+iter_1[19][1])/2+(iter_1[2][1]+iter_1[2][2])/2)/8;
v_2[3][1] = v_2[2][0]; 

v_2[0][2] = v_2[3][1]; //face3
v_2[1][2] = v_2[2][1];
v_2[2][2] = iter_1[2][2]/4 + (q_2[2]+q_2[19]+q_2[9])/12 +       ((iter_1[2][2]+iter_1[2][3])/2+(iter_1[2][2]+iter_1[19][0])/2+(iter_1[2][2]+iter_1[9][2])/2)/6;
v_2[3][2] = iter_1[2][3]/4 + (q_2[2]+q_2[9]+q_2[8]+q_2[3])/16 + ((iter_1[2][3]+iter_1[2][0])/2+(iter_1[2][3]+iter_1[9][1])/2+(iter_1[2][3]+iter_1[8][2])/2+(iter_1[2][3]+iter_1[3][3])/2)/8;

v_2[0][3] = v_2[3][0]; //face4
v_2[1][3] = v_2[3][1];
v_2[2][3] = v_2[3][2];
v_2[3][3] = iter_1[3][3]/4 + (q_2[3]+q_2[8]+q_2[6])/12 + ((iter_1[3][3]+iter_1[3][0])/2+(iter_1[3][3]+iter_1[8][1])/2+(iter_1[3][3]+iter_1[6][3])/2)/6;

v_2[0][4] = iter_1[4][0]/4 + (q_2[4]+q_2[13] +q_2[20])/12 +         ((iter_1[4][0]+iter_1[4][1])/2+(iter_1[4][0]+iter_1[13][2])/2 +(iter_1[4][0]+iter_1[20][1])/2)/6; //face5
v_2[1][4] = iter_1[4][1]/4 + (q_2[4]+q_2[20] +q_2[23]+q_2[5])/16 +  ((iter_1[4][1]+iter_1[4][2])/2+(iter_1[4][1]+iter_1[20][0])/2+(iter_1[4][1]+iter_1[23][1])/2+(iter_1[4][1]+iter_1[5][1])/2)/8;
v_2[2][4] = iter_1[4][2]/4 + (q_2[4]+q_2[5]  +q_2[6] +q_2[7])/16 +  ((iter_1[4][2]+iter_1[4][3])/2+(iter_1[4][2]+iter_1[5][0])/2 +(iter_1[4][2]+iter_1[6][1])/2+(iter_1[4][2]+iter_1[7][2])/2)/8;
v_2[3][4] = iter_1[4][3]/4 + (q_2[4]+q_2[7]  +q_2[14]+q_2[13])/16 + ((iter_1[4][3]+iter_1[4][0])/2+(iter_1[4][3]+iter_1[7][1])/2 +(iter_1[4][3]+iter_1[14][2])/2+(iter_1[4][3]+iter_1[13][3])/2)/8;

v_2[0][5] = v_2[1][4]; //face6 
v_2[1][5] = v_2[0][0];
v_2[2][5] = v_2[3][0];
v_2[3][5] = v_2[2][4]; 

v_2[0][6] = v_2[3][5]; //face7
v_2[1][6] = v_2[2][5];
v_2[2][6] = v_2[3][3];
v_2[3][6] = iter_1[6][3]/4 + (q_2[6]+q_2[8]+q_2[11]+q_2[7])/16 + ((iter_1[6][3]+iter_1[6][0])/2+(iter_1[6][3]+iter_1[8][0])/2+(iter_1[6][3]+iter_1[11][1])/2+(iter_1[6][3]+iter_1[7][3])/2)/8;

v_2[0][7] = v_2[3][4]; //face8
v_2[1][7] = v_2[3][5];
v_2[2][7] = v_2[3][6];
v_2[3][7] = iter_1[7][3]/4 + (q_2[7]+q_2[11]+q_2[14])/12 + ((iter_1[7][3]+iter_1[7][0])/2+(iter_1[7][3]+iter_1[14][3])/2+(iter_1[7][3]+iter_1[11][0])/2)/6;

v_2[0][8] = v_2[3][3]; //face9
v_2[1][8] = v_2[2][3];
v_2[2][8] = iter_1[8][2]/4 + (q_2[8]+q_2[9] +q_2[10] +q_2[11])/16 +  ((iter_1[8][2]+iter_1[8][3])/2+(iter_1[8][2]+iter_1[9][0])/2 +(iter_1[8][2]+iter_1[10][1])/2+(iter_1[8][2]+iter_1[11][2])/2)/8;
v_2[3][8] = v_2[3][6];

v_2[0][9] = v_2[1][8]; //face10 
v_2[1][9] = v_2[2][2];
v_2[2][9] = iter_1[9][2]/4 + (q_2[9]+q_2[19]+q_2[18]+q_2[10])/16 + ((iter_1[9][2]+iter_1[9][3])/2+(iter_1[9][2]+iter_1[19][3])/2+(iter_1[9][2]+iter_1[18][0])/2+(iter_1[9][2]+iter_1[10][2])/2)/8;
v_2[3][9] = v_2[2][8];

v_2[0][10] = v_2[3][9]; //face11
v_2[1][10] = v_2[2][9];
v_2[2][10] = iter_1[10][2]/4 + (q_2[10]+q_2[18]+q_2[15])/12         + ((iter_1[10][2]+iter_1[10][3])/2+(iter_1[10][2]+iter_1[18][3])/2+(iter_1[10][2]+iter_1[15][0])/2)/6;
v_2[3][10] = iter_1[10][3]/4 + (q_2[10]+q_2[15]+q_2[14]+q_2[11])/16 + ((iter_1[10][3]+iter_1[10][0])/2+(iter_1[10][3]+iter_1[15][3])/2+(iter_1[10][3]+iter_1[14][0])/2+(iter_1[10][3]+iter_1[11][3])/2)/8;

v_2[0][11] = v_2[3][8]; //face12
v_2[1][11] = v_2[3][9];
v_2[2][11] = v_2[3][10];
v_2[3][11] = v_2[3][7];

v_2[0][12] = iter_1[12][0]/4 + (q_2[12]+q_2[17]+q_2[21])/12 +          ((iter_1[12][0]+iter_1[12][1])/2+(iter_1[12][0]+iter_1[17][2])/2 +(iter_1[12][0]+iter_1[21][2])/2)/6; //face13
v_2[1][12] = iter_1[12][1]/4 + (q_2[12]+q_2[21]+q_2[20]+q_2[13])/16 +  ((iter_1[12][1]+iter_1[12][2])/2+(iter_1[12][1]+iter_1[21][1])/2+(iter_1[12][1]+iter_1[20][2])/2+(iter_1[12][1]+iter_1[13][1])/2)/8;
v_2[2][12] = iter_1[12][2]/4 + (q_2[12]+q_2[13]+q_2[14]+q_2[15])/16 +  ((iter_1[12][2]+iter_1[12][3])/2+(iter_1[12][2]+iter_1[13][0])/2 +(iter_1[12][2]+iter_1[14][1])/2+(iter_1[12][2]+iter_1[15][2])/2)/8;
v_2[3][12] = iter_1[12][3]/4 + (q_2[12]+q_2[15]+q_2[18]+q_2[17])/16 +  ((iter_1[12][3]+iter_1[12][0])/2+(iter_1[12][3]+iter_1[15][1])/2 +(iter_1[12][3]+iter_1[18][2])/2+(iter_1[12][3]+iter_1[17][3])/2)/8;

v_2[0][13] = v_2[1][12]; //face14
v_2[1][13] = v_2[0][4];
v_2[2][13] = v_2[3][4];
v_2[3][13] = v_2[2][12];

v_2[0][14] = v_2[3][13]; //face15
v_2[1][14] = v_2[2][13];
v_2[2][14] = v_2[3][7];
v_2[3][14] = v_2[3][10];

v_2[0][15] = v_2[3][12]; //face16
v_2[1][15] = v_2[3][13];
v_2[2][15] = v_2[3][14];
v_2[3][15] = v_2[2][10];

v_2[0][16] = v_2[1][1]; //face17
v_2[1][16] = iter_1[16][1]/4 + (q_2[16]+q_2[22]+q_2[21]+q_2[17])/16 +  ((iter_1[16][1]+iter_1[16][2])/2+(iter_1[16][1]+iter_1[22][2])/2+(iter_1[16][1]+iter_1[21][3])/2+(iter_1[16][1]+iter_1[17][1])/2)/8;
v_2[2][16] = iter_1[16][2]/4 + (q_2[16]+q_2[17]+q_2[18]+q_2[19])/16 +  ((iter_1[16][2]+iter_1[16][3])/2+(iter_1[16][2]+iter_1[17][0])/2 +(iter_1[16][2]+iter_1[18][1])/2+(iter_1[16][2]+iter_1[19][2])/2)/8;
v_2[3][16] = v_2[2][1];

v_2[0][17] = v_2[1][16]; //face18
v_2[1][17] = v_2[0][12];
v_2[2][17] = v_2[3][12];
v_2[3][17] = v_2[2][16];

v_2[0][18] = v_2[3][17]; //face19
v_2[1][18] = v_2[2][17];
v_2[2][18] = v_2[3][15];
v_2[3][18] = v_2[2][9];

v_2[0][19] = v_2[3][16]; //face20
v_2[1][19] = v_2[3][17];
v_2[2][19] = v_2[3][18];
v_2[3][19] = v_2[2][2];

v_2[0][20] = v_2[1][13]; //face20
v_2[1][20] = v_2[0][13];
v_2[2][20] = iter_1[20][2]/4 + (q_2[20]+q_2[21]+q_2[22]+q_2[23])/16 +  ((iter_1[20][2]+iter_1[20][3])/2+(iter_1[20][2]+iter_1[21][0])/2 +(iter_1[20][2]+iter_1[22][1])/2+(iter_1[20][2]+iter_1[23][2])/2)/8;
v_2[3][20] = v_2[1][4];

v_2[0][21] = v_2[1][20]; //face21
v_2[1][21] = v_2[1][17];
v_2[2][21] = v_2[0][17];
v_2[3][21] = v_2[2][20];

v_2[0][22] = v_2[3][21]; //face22
v_2[1][22] = v_2[2][21];
v_2[2][22] = v_2[0][16];
v_2[3][22] = v_2[0][1];

v_2[0][23] = v_2[3][20]; //face23
v_2[1][23] = v_2[3][21];
v_2[2][23] = v_2[3][22];
v_2[3][23] = v_2[0][0];

 return;
}

void montaVetor2(void)
{
 int a=0;
 for (int j = 0; j < 96; j++)
 { 
       iter_2[j][0] = v_2[0][a];
       iter_2[j][1] = t_2[0][a];
       iter_2[j][2] = q_2[a];
       iter_2[j][3] = t_2[3][a];
       j++;
       
       iter_2[j][0] = t_2[0][a];
       iter_2[j][1] = v_2[1][a];
       iter_2[j][2] = t_2[1][a];
       iter_2[j][3] = q_2[a];
       j++;
       
       iter_2[j][0] = q_2[a];
       iter_2[j][1] = t_2[1][a];
       iter_2[j][2] = v_2[2][a];
       iter_2[j][3] = t_2[2][a];
       j++;

       iter_2[j][0] = t_2[3][a];
       iter_2[j][1] = q_2[a];
       iter_2[j][2] = t_2[2][a];
       iter_2[j][3] = v_2[3][a];
       a++;
 }

 return;
}

void iteracao3(void)
{
 //pontos nas faces
for (int j = 0; j <96; j++)
 {
    q_3[j] = (iter_2[j][0] + iter_2[j][1] + iter_2[j][2] + iter_2[j][3])/4;
 }
 
 //pontos nas linhas de intersecção
for (int j = 0; j <96; j++)
 {
     t_3[0][j] = (q_3[j]+q_3[aux_t3[j][0]])/4 + (iter_2[j][0]+iter_2[j][1])/4;
     t_3[1][j] = (q_3[j]+q_3[aux_t3[j][1]])/4 + (iter_2[j][1]+iter_2[j][2])/4;
     t_3[2][j] = (q_3[j]+q_3[aux_t3[j][2]])/4 + (iter_2[j][2]+iter_2[j][3])/4;
     t_3[3][j] = (q_3[j]+q_3[aux_t3[j][3]])/4 + (iter_2[j][3]+iter_2[j][0])/4;
 }
 
 //pontos de vértice = Q/4+2R/n+S(n-3)/n
for (int j = 0; j <96; j++)//face j
 {
if (aux_v3[j][0][3] == -1) 
v_3[0][j] = iter_2[j][0]/4 + (q_3[j]+q_3[aux_v3[j][0][1]] +q_3[aux_v3[j][0][2]])/12 +                      ((iter_2[j][0]+iter_2[j][1])/2+(iter_2[j][0]+iter_2[aux_v3[j][0][1]][2])/2 +(iter_2[j][0]+iter_2[aux_v3[j][0][2]][0])/2)/6;
else
v_3[0][j] = iter_2[j][0]/4 + (q_3[j]+q_3[aux_v3[j][0][1]] +q_3[aux_v3[j][0][2]]+q_3[aux_v3[j][0][3]])/16 + ((iter_2[j][0]+iter_2[j][1])/2+(iter_2[j][0]+iter_2[aux_v3[j][0][1]][2])/2 +(iter_2[j][0]+iter_2[aux_v3[j][0][2]][3])/2 +(iter_2[j][0]+iter_2[aux_v3[j][0][3]][0])/2)/8;

if (aux_v3[j][1][3] == -1)
v_3[1][j] = iter_2[j][1]/4 + (q_3[j]+q_3[aux_v3[j][1][1]] +q_3[aux_v3[j][1][2]])/12 +                      ((iter_2[j][1]+iter_2[j][2])/2+(iter_2[j][1]+iter_2[aux_v3[j][1][1]][3])/2 +(iter_2[j][1]+iter_2[aux_v3[j][1][2]][1])/2)/6;
else
v_3[1][j] = iter_2[j][1]/4 + (q_3[j]+q_3[aux_v3[j][1][1]] +q_3[aux_v3[j][1][2]]+q_3[aux_v3[j][1][3]])/16 + ((iter_2[j][1]+iter_2[j][2])/2+(iter_2[j][1]+iter_2[aux_v3[j][1][1]][3])/2 +(iter_2[j][1]+iter_2[aux_v3[j][1][2]][0])/2+(iter_2[j][1]+iter_2[aux_v3[j][1][3]][1])/2)/8;

if (aux_v3[j][2][3] == -1) 
v_3[2][j] = iter_2[j][2]/4 + (q_3[j]+q_3[aux_v3[j][2][1]] +q_3[aux_v3[j][2][2]])/12 +                      ((iter_2[j][2]+iter_2[j][3])/2+(iter_2[j][2]+iter_2[aux_v3[j][2][1]][0])/2 +(iter_2[j][2]+iter_2[aux_v3[j][2][2]][1])/2)/6;
else
v_3[2][j] = iter_2[j][2]/4 + (q_3[j]+q_3[aux_v3[j][2][1]] +q_3[aux_v3[j][2][2]]+q_3[aux_v3[j][2][3]])/16 + ((iter_2[j][2]+iter_2[j][3])/2+(iter_2[j][2]+iter_2[aux_v3[j][2][1]][0])/2 +(iter_2[j][2]+iter_2[aux_v3[j][2][2]][1])/2+(iter_2[j][2]+iter_2[aux_v3[j][2][3]][2])/2)/8;

if (aux_v3[j][3][3] == -1)
v_3[3][j] = iter_2[j][3]/4 + (q_3[j]+q_3[aux_v3[j][3][1]] +q_3[aux_v3[j][3][2]])/12 +                      ((iter_2[j][3]+iter_2[j][0])/2+(iter_2[j][3]+iter_2[aux_v3[j][3][1]][1])/2 +(iter_2[j][3]+iter_2[aux_v3[j][3][2]][2])/2)/6;
else
v_3[3][j] = iter_2[j][3]/4 + (q_3[j]+q_3[aux_v3[j][3][1]] +q_3[aux_v3[j][3][2]]+q_3[aux_v3[j][3][3]])/16 + ((iter_2[j][3]+iter_2[j][0])/2+(iter_2[j][3]+iter_2[aux_v3[j][3][1]][1])/2 +(iter_2[j][3]+iter_2[aux_v3[j][3][2]][2])/2+(iter_2[j][3]+iter_2[aux_v3[j][3][3]][3])/2)/8;
}

v_3[3][95] = v_3[1][21] = v_3[0][0];
v_3[0][64] = v_3[2][90] = v_3[1][5];
v_3[1][37] = v_3[3][79] = v_3[2][10];
v_3[2][26] = v_3[0][32] = v_3[3][15];

v_3[3][31] = v_3[2][58] = v_3[3][47];
v_3[1][53] = v_3[0][80] = v_3[0][16];
v_3[2][42] = v_3[3][63] = v_3[2][74];
v_3[0][48] = v_3[1][85] = v_3[1][69];

//tratamento das (grandes) faces que se tocam
v_3[3][44] = iter_2[44][3]/4 + (q_3[44]+q_3[47] +q_3[31]+q_3[30])/16 + ((iter_2[44][3]+iter_2[44][0])/2+(iter_2[44][3]+iter_2[47][1])/2 +(iter_2[44][3]+iter_2[31][1])/2+(iter_2[44][3]+iter_2[30][0])/2)/8;
v_3[3][35] = iter_2[35][3]/4 + (q_3[35]+q_3[44] +q_3[30]+q_3[27])/16 + ((iter_2[35][3]+iter_2[35][0])/2+(iter_2[35][3]+iter_2[44][1])/2 +(iter_2[35][3]+iter_2[30][1])/2+(iter_2[35][3]+iter_2[27][0])/2)/8;
v_3[3][32] = iter_2[32][3]/4 + (q_3[32]+q_3[35] +q_3[27]+q_3[26])/16 + ((iter_2[32][3]+iter_2[32][0])/2+(iter_2[32][3]+iter_2[35][1])/2 +(iter_2[32][3]+iter_2[27][1])/2+(iter_2[32][3]+iter_2[26][0])/2)/8;
v_3[2][31] = v_3[3][30] = v_3[0][47] = v_3[3][44];
v_3[2][30] = v_3[3][27] = v_3[0][44] = v_3[3][35];
v_3[2][27] = v_3[3][26] = v_3[0][35] = v_3[3][32];

v_3[2][37] = iter_2[37][2]/4 + (q_3[37]+q_3[38] +q_3[78]+q_3[79])/16 + ((iter_2[37][2]+iter_2[37][3])/2+(iter_2[37][2]+iter_2[79][0])/2 +(iter_2[37][2]+iter_2[78][0])/2+(iter_2[37][2]+iter_2[38][2])/2)/8;
v_3[2][38] = iter_2[38][2]/4 + (q_3[38]+q_3[41] +q_3[75]+q_3[78])/16 + ((iter_2[38][2]+iter_2[38][3])/2+(iter_2[38][2]+iter_2[78][0])/2 +(iter_2[38][2]+iter_2[75][0])/2+(iter_2[38][2]+iter_2[41][2])/2)/8;
v_3[2][41] = iter_2[41][2]/4 + (q_3[41]+q_3[42] +q_3[74]+q_3[75])/16 + ((iter_2[41][2]+iter_2[41][3])/2+(iter_2[41][2]+iter_2[75][0])/2 +(iter_2[41][2]+iter_2[74][0])/2+(iter_2[41][2]+iter_2[42][2])/2)/8;
v_3[2][79] = v_3[3][78] = v_3[1][38] = v_3[2][37];
v_3[2][78] = v_3[3][75] = v_3[1][41] = v_3[2][38];
v_3[2][75] = v_3[3][74] = v_3[1][42] = v_3[2][41];

v_3[2][43] = iter_2[43][2]/4 + (q_3[43]+q_3[42] +q_3[62]+q_3[63])/16 + ((iter_2[43][2]+iter_2[43][3])/2+(iter_2[43][2]+iter_2[42][0])/2 +(iter_2[43][2]+iter_2[63][3])/2+(iter_2[43][2]+iter_2[62][0])/2)/8;
v_3[2][46] = iter_2[46][2]/4 + (q_3[46]+q_3[43] +q_3[59]+q_3[62])/16 + ((iter_2[46][2]+iter_2[46][3])/2+(iter_2[46][2]+iter_2[43][0])/2 +(iter_2[46][2]+iter_2[62][3])/2+(iter_2[46][2]+iter_2[59][0])/2)/8;
v_3[2][47] = iter_2[47][2]/4 + (q_3[47]+q_3[46] +q_3[58]+q_3[59])/16 + ((iter_2[47][2]+iter_2[47][3])/2+(iter_2[47][2]+iter_2[46][0])/2 +(iter_2[47][2]+iter_2[59][3])/2+(iter_2[47][2]+iter_2[58][0])/2)/8;
v_3[2][63] = v_3[3][62] = v_3[3][42] = v_3[2][43];
v_3[2][62] = v_3[3][59] = v_3[3][43] = v_3[2][46];
v_3[2][59] = v_3[3][58] = v_3[3][46] = v_3[2][47];

v_3[0][83] = iter_2[83][0]/4 + (q_3[83]+q_3[80] +q_3[17]+q_3[16])/16 + ((iter_2[83][0]+iter_2[83][1])/2+(iter_2[83][0]+iter_2[80][0])/2 +(iter_2[83][0]+iter_2[16][2])/2 +(iter_2[83][0]+iter_2[17][1])/2)/8;
v_3[0][92] = iter_2[92][0]/4 + (q_3[92]+q_3[83] +q_3[20]+q_3[17])/16 + ((iter_2[92][0]+iter_2[92][1])/2+(iter_2[92][0]+iter_2[83][0])/2 +(iter_2[92][0]+iter_2[17][2])/2 +(iter_2[92][0]+iter_2[20][1])/2)/8;
v_3[0][95] = iter_2[95][0]/4 + (q_3[95]+q_3[92] +q_3[21]+q_3[20])/16 + ((iter_2[95][0]+iter_2[95][1])/2+(iter_2[95][0]+iter_2[92][0])/2 +(iter_2[95][0]+iter_2[20][2])/2 +(iter_2[95][0]+iter_2[21][1])/2)/8;
v_3[1][16] = v_3[0][17] = v_3[3][80] = v_3[0][83];
v_3[1][17] = v_3[0][20] = v_3[3][83] = v_3[0][92];
v_3[1][20] = v_3[0][21] = v_3[3][92] = v_3[0][95];

v_3[2][89] = iter_2[89][2]/4 + (q_3[89]+q_3[90] +q_3[65]+q_3[64])/16 + ((iter_2[89][2]+iter_2[89][3])/2+(iter_2[89][2]+iter_2[90][2])/2 +(iter_2[89][2]+iter_2[64][2])/2+(iter_2[89][2]+iter_2[65][1])/2)/8;
v_3[2][86] = iter_2[86][2]/4 + (q_3[86]+q_3[89] +q_3[68]+q_3[65])/16 + ((iter_2[86][2]+iter_2[86][3])/2+(iter_2[86][2]+iter_2[89][2])/2 +(iter_2[86][2]+iter_2[65][2])/2+(iter_2[86][2]+iter_2[68][1])/2)/8;
v_3[2][85] = iter_2[85][2]/4 + (q_3[85]+q_3[86] +q_3[69]+q_3[68])/16 + ((iter_2[85][2]+iter_2[85][3])/2+(iter_2[85][2]+iter_2[86][2])/2 +(iter_2[85][2]+iter_2[68][2])/2+(iter_2[85][2]+iter_2[69][1])/2)/8;
v_3[1][64] = v_3[0][65] = v_3[1][90] = v_3[2][89];
v_3[1][65] = v_3[0][68] = v_3[1][89] = v_3[2][86];
v_3[1][68] = v_3[0][69] = v_3[1][86] = v_3[2][85];

v_3[1][52] = iter_2[52][1]/4 + (q_3[52]+q_3[53] +q_3[81]+q_3[80])/16 + ((iter_2[52][1]+iter_2[52][2])/2+(iter_2[52][1]+iter_2[53][1])/2 +(iter_2[52][1]+iter_2[81][1])/2+(iter_2[52][1]+iter_2[80][2])/2)/8;
v_3[1][49] = iter_2[49][1]/4 + (q_3[49]+q_3[52] +q_3[84]+q_3[81])/16 + ((iter_2[49][1]+iter_2[49][2])/2+(iter_2[49][1]+iter_2[52][1])/2 +(iter_2[49][1]+iter_2[84][1])/2+(iter_2[49][1]+iter_2[81][2])/2)/8;
v_3[1][48] = iter_2[48][1]/4 + (q_3[48]+q_3[49] +q_3[85]+q_3[84])/16 + ((iter_2[48][1]+iter_2[48][2])/2+(iter_2[48][1]+iter_2[49][1])/2 +(iter_2[48][1]+iter_2[85][1])/2+(iter_2[48][1]+iter_2[84][2])/2)/8;
v_3[1][80] = v_3[0][81] = v_3[0][53] = v_3[1][52];
v_3[1][81] = v_3[0][84] = v_3[0][52] = v_3[1][49];
v_3[1][84] = v_3[0][85] = v_3[0][49] = v_3[1][48];

 return;
}
     
void tetraedroIter1(void)
{
  for (int c = 0; c < 4; c++)
  {
      ptosTet[c][0].x = te[c][0][0]; ptosTet[c][0].y = te[c][0][1];ptosTet[c][0].z = te[c][0][2];
      ptosTet[c][1].x = te[c][1][0]; ptosTet[c][1].y = te[c][1][1];ptosTet[c][1].z = te[c][1][2];
      ptosTet[c][2].x = te[c][2][0]; ptosTet[c][2].y = te[c][2][1];ptosTet[c][2].z = te[c][2][2];
  }
    
     for (int c = 0; c < 4; c++)
     {
         qt[c] = (ptosTet[c][0]+ptosTet[c][1]+ptosTet[c][2])/3;
     }

e[0][0] = (qt[0] + qt[3])/4 + (ptosTet[0][0] + ptosTet[0][1])/4;
e[1][0] = (qt[0] + qt[1])/4 + (ptosTet[0][1] + ptosTet[0][2])/4;
e[2][0] = (qt[0] + qt[2])/4 + (ptosTet[0][2] + ptosTet[0][0])/4;

e[0][1] = (qt[1] + qt[3])/4 + (ptosTet[1][0] + ptosTet[1][1])/4;
e[1][1] = (qt[1] + qt[2])/4 + (ptosTet[1][1] + ptosTet[1][2])/4;
e[2][1] = (qt[1] + qt[0])/4 + (ptosTet[1][2] + ptosTet[1][0])/4;

e[0][2] = (qt[2] + qt[0])/4 + (ptosTet[2][0] + ptosTet[2][1])/4;
e[1][2] = (qt[2] + qt[1])/4 + (ptosTet[2][1] + ptosTet[2][2])/4;
e[2][2] = (qt[2] + qt[3])/4 + (ptosTet[2][2] + ptosTet[2][0])/4;

e[0][3] = (qt[3] + qt[2])/4 + (ptosTet[3][0] + ptosTet[3][1])/4;
e[1][3] = (qt[3] + qt[1])/4 + (ptosTet[3][1] + ptosTet[3][2])/4;
e[2][3] = (qt[3] + qt[0])/4 + (ptosTet[3][2] + ptosTet[3][0])/4;


ve[0][0] = ptosTet[0][0]/4 + (qt[0]+qt[3]+qt[2])/12 + ((ptosTet[0][0] + ptosTet[0][1])/2 +(ptosTet[0][0] + ptosTet[2][1])/2+(ptosTet[0][0] + ptosTet[3][1])/2)/6;
ve[1][0] = ptosTet[0][1]/4 + (qt[0]+qt[3]+qt[1])/12 + ((ptosTet[0][1] + ptosTet[0][2])/2 +(ptosTet[0][1] + ptosTet[1][1])/2+(ptosTet[0][1] + ptosTet[3][0])/2)/6;
ve[2][0] = ptosTet[0][2]/4 + (qt[0]+qt[1]+qt[2])/12 + ((ptosTet[0][2] + ptosTet[0][0])/2 +(ptosTet[0][2] + ptosTet[2][2])/2+(ptosTet[0][2] + ptosTet[1][0])/2)/6;

ve[0][1] = ve[1][0];
ve[1][1] = ptosTet[1][1]/4 + (qt[1]+qt[3]+qt[2])/12 + ((ptosTet[1][1] + ptosTet[1][2])/2 +(ptosTet[1][1] + ptosTet[3][2])/2+(ptosTet[1][1] + ptosTet[2][0])/2)/6;
ve[2][1] = ve[2][0];

ve[0][2] = ve[0][0];
ve[1][2] = ve[2][0];
ve[2][2] = ve[1][1];

ve[0][3] = ve[0][2];
ve[1][3] = ve[2][2];
ve[2][3] = ve[0][1];

}   
     
void tetraedroIter2(void)
{
      //pontos nas faces
 for (int j = 0; j <12; j++)
 {
    qt_2[j] = (iterTe_1[j][0] + iterTe_1[j][1] + iterTe_1[j][2] + iterTe_1[j][3])/4;
 }

 //pontos nas linhas de intersecção
e_2[0][0] = (qt_2[0]+qt_2[9])/4 + (iterTe_1[0][0]+iterTe_1[0][1])/4; //face 1 (de 12)
e_2[1][0] = (qt_2[0]+qt_2[1])/4 + (iterTe_1[0][1]+iterTe_1[0][2])/4;
e_2[2][0] = (qt_2[0]+qt_2[2])/4 + (iterTe_1[0][2]+iterTe_1[0][3])/4;
e_2[3][0] = (qt_2[0]+qt_2[6])/4 + (iterTe_1[0][3]+iterTe_1[0][0])/4;

e_2[0][1] = (qt_2[1]+qt_2[11])/4  + (iterTe_1[1][0]+iterTe_1[1][1])/4; //face 2 (de 12)
e_2[1][1] = (qt_2[1]+qt_2[3])/4 + (iterTe_1[1][1]+iterTe_1[1][2])/4;
e_2[2][1] = (qt_2[1]+qt_2[2])/4  + (iterTe_1[1][2]+iterTe_1[1][3])/4;
e_2[3][1] = (qt_2[1]+qt_2[0])/4  + (iterTe_1[1][3]+iterTe_1[1][0])/4;

e_2[0][2] = (qt_2[2]+qt_2[1])/4 + (iterTe_1[2][0]+iterTe_1[2][1])/4; //face 3 (de 12)
e_2[1][2] = (qt_2[2]+qt_2[5])/4 + (iterTe_1[2][1]+iterTe_1[2][2])/4;
e_2[2][2] = (qt_2[2]+qt_2[7])/4 + (iterTe_1[2][2]+iterTe_1[2][3])/4;
e_2[3][2] = (qt_2[2]+qt_2[0])/4 + (iterTe_1[2][3]+iterTe_1[2][0])/4;

e_2[0][3] = (qt_2[3]+qt_2[11])/4  + (iterTe_1[3][0]+iterTe_1[3][1])/4; //face 4 (de 12)
e_2[1][3] = (qt_2[3]+qt_2[4])/4 + (iterTe_1[3][1]+iterTe_1[3][2])/4;
e_2[2][3] = (qt_2[3]+qt_2[5])/4  + (iterTe_1[3][2]+iterTe_1[3][3])/4;
e_2[3][3] = (qt_2[3]+qt_2[1])/4  + (iterTe_1[3][3]+iterTe_1[3][0])/4;

e_2[0][4] = (qt_2[4]+qt_2[10])/4 + (iterTe_1[4][0]+iterTe_1[4][1])/4; //face 5 (de 12)
e_2[1][4] = (qt_2[4]+qt_2[8])/4  + (iterTe_1[4][1]+iterTe_1[4][2])/4;
e_2[2][4] = (qt_2[4]+qt_2[5])/4  + (iterTe_1[4][2]+iterTe_1[4][3])/4;
e_2[3][4] = (qt_2[4]+qt_2[3])/4  + (iterTe_1[4][3]+iterTe_1[4][0])/4;

e_2[0][5] = (qt_2[5]+qt_2[4])/4 + (iterTe_1[5][0]+iterTe_1[5][1])/4; //face 6 (de 12)
e_2[1][5] = (qt_2[5]+qt_2[7])/4 + (iterTe_1[5][1]+iterTe_1[5][2])/4;
e_2[2][5] = (qt_2[5]+qt_2[2])/4 + (iterTe_1[5][2]+iterTe_1[5][3])/4;
e_2[3][5] = (qt_2[5]+qt_2[3])/4 + (iterTe_1[5][3]+iterTe_1[5][0])/4;

e_2[0][6] = (qt_2[6]+qt_2[0])/4 + (iterTe_1[6][0]+iterTe_1[6][1])/4; //face 7 (de 12)
e_2[1][6] = (qt_2[6]+qt_2[7])/4  + (iterTe_1[6][1]+iterTe_1[6][2])/4;
e_2[2][6] = (qt_2[6]+qt_2[8])/4  + (iterTe_1[6][2]+iterTe_1[6][3])/4;
e_2[3][6] = (qt_2[6]+qt_2[9])/4  + (iterTe_1[6][3]+iterTe_1[6][0])/4;

e_2[0][7] = (qt_2[7]+qt_2[2])/4  + (iterTe_1[7][0]+iterTe_1[7][1])/4; //face 8 (de 12)
e_2[1][7] = (qt_2[7]+qt_2[5])/4 + (iterTe_1[7][1]+iterTe_1[7][2])/4;
e_2[2][7] = (qt_2[7]+qt_2[8])/4  + (iterTe_1[7][2]+iterTe_1[7][3])/4;
e_2[3][7] = (qt_2[7]+qt_2[6])/4  + (iterTe_1[7][3]+iterTe_1[7][0])/4;

e_2[0][8] = (qt_2[8]+qt_2[7])/4 + (iterTe_1[8][0]+iterTe_1[8][1])/4; //face 9 (de 12)
e_2[1][8] = (qt_2[8]+qt_2[4])/4 + (iterTe_1[8][1]+iterTe_1[8][2])/4;
e_2[2][8] = (qt_2[8]+qt_2[10])/4 + (iterTe_1[8][2]+iterTe_1[8][3])/4;
e_2[3][8] = (qt_2[8]+qt_2[6])/4 + (iterTe_1[8][3]+iterTe_1[8][0])/4;

e_2[0][9] = (qt_2[9]+qt_2[6])/4  + (iterTe_1[9][0]+iterTe_1[9][1])/4; //face 10 (de 12)
e_2[1][9] = (qt_2[9]+qt_2[10])/4 + (iterTe_1[9][1]+iterTe_1[9][2])/4;
e_2[2][9] = (qt_2[9]+qt_2[11])/4 + (iterTe_1[9][2]+iterTe_1[9][3])/4;
e_2[3][9] = (qt_2[9]+qt_2[0])/4  + (iterTe_1[9][3]+iterTe_1[9][0])/4;

e_2[0][10] = (qt_2[10]+qt_2[8])/4  + (iterTe_1[10][0]+iterTe_1[10][1])/4; //face 11 (de 12)
e_2[1][10] = (qt_2[10]+qt_2[4])/4 + (iterTe_1[10][1]+iterTe_1[10][2])/4;
e_2[2][10] = (qt_2[10]+qt_2[11])/4  + (iterTe_1[10][2]+iterTe_1[10][3])/4;
e_2[3][10] = (qt_2[10]+qt_2[9])/4  + (iterTe_1[10][3]+iterTe_1[10][0])/4;

e_2[0][11] = (qt_2[11]+qt_2[10])/4 + (iterTe_1[11][0]+iterTe_1[11][1])/4; //face 12 (de 12)
e_2[1][11] = (qt_2[11]+qt_2[3])/4 + (iterTe_1[11][1]+iterTe_1[11][2])/4;
e_2[2][11] = (qt_2[11]+qt_2[1])/4 + (iterTe_1[11][2]+iterTe_1[11][3])/4;
e_2[3][11] = (qt_2[11]+qt_2[9])/4 + (iterTe_1[11][3]+iterTe_1[11][0])/4;


ve_2[0][0] = iterTe_1[0][0]/4 + (qt_2[0]+qt_2[6] +qt_2[9])/12 +        ((iterTe_1[0][0]+iterTe_1[0][1])/2+(iterTe_1[0][0]+iterTe_1[6][1])/2 +(iterTe_1[0][0]+iterTe_1[9][1])/2)/6; //face1
ve_2[1][0] = iterTe_1[0][1]/4 + (qt_2[0]+qt_2[9]+qt_2[11]+qt_2[1])/16 + ((iterTe_1[0][1]+iterTe_1[0][2])/2+(iterTe_1[0][1]+iterTe_1[9][0])/2+(iterTe_1[0][1]+iterTe_1[11][0])/2+(iterTe_1[0][1]+iterTe_1[1][1])/2)/8;
ve_2[2][0] = iterTe_1[0][2]/4 + (qt_2[0]+qt_2[1] +qt_2[2])/12 +  ((iterTe_1[0][2]+iterTe_1[0][3])/2+(iterTe_1[0][2]+iterTe_1[1][0])/2 +(iterTe_1[0][2]+iterTe_1[2][1])/2)/6;
ve_2[3][0] = iterTe_1[0][3]/4 + (qt_2[0]+qt_2[2] +qt_2[7]+qt_2[6])/16 +  ((iterTe_1[0][3]+iterTe_1[0][0])/2+(iterTe_1[0][3]+iterTe_1[2][0])/2 +(iterTe_1[0][3]+iterTe_1[7][2])/2+(iterTe_1[0][3]+iterTe_1[6][2])/2)/8;

ve_2[0][1] = ve_2[1][0]; //face2
ve_2[1][1] = iterTe_1[1][1]/4 + (qt_2[1]+qt_2[11]+qt_2[3])/12 +        ((iterTe_1[1][1]+iterTe_1[1][2])/2+(iterTe_1[1][1]+iterTe_1[11][3])/2+(iterTe_1[1][1]+iterTe_1[3][1])/2)/6;
ve_2[2][1] = iterTe_1[1][2]/4 + (qt_2[1]+qt_2[3]+qt_2[5]+qt_2[2])/16 + ((iterTe_1[1][2]+iterTe_1[1][3])/2+(iterTe_1[1][2]+iterTe_1[3][0])/2+(iterTe_1[1][2]+iterTe_1[5][0])/2+(iterTe_1[1][2]+iterTe_1[2][2])/2)/8;
ve_2[3][1] = ve_2[2][0];

ve_2[0][2] = ve_2[3][1]; //face3
ve_2[1][2] = ve_2[2][1];
ve_2[2][2] = iterTe_1[2][2]/4 + (qt_2[2]+qt_2[5]+qt_2[7])/12 +       ((iterTe_1[2][2]+iterTe_1[2][3])/2+(iterTe_1[2][2]+iterTe_1[5][3])/2+(iterTe_1[2][2]+iterTe_1[7][2])/2)/6;
ve_2[3][2] = ve_2[3][0];

ve_2[0][3] = ve_2[1][1]; //face4
ve_2[1][3] = iterTe_1[3][1]/4 + (qt_2[3]+qt_2[11]+qt_2[10]+qt_2[5])/16 + ((iterTe_1[3][1]+iterTe_1[3][2])/2+(iterTe_1[3][1]+iterTe_1[10][1])/2+(iterTe_1[3][1]+iterTe_1[11][2])/2+(iterTe_1[3][1]+iterTe_1[4][1])/2)/8;
ve_2[2][3] = iterTe_1[3][2]/4 + (qt_2[3]+qt_2[4] +qt_2[5])/12 +  ((iterTe_1[3][2]+iterTe_1[3][3])/2+(iterTe_1[3][2]+iterTe_1[4][0])/2 +(iterTe_1[3][2]+iterTe_1[5][1])/2)/6;
ve_2[3][3] = ve_2[2][1];

ve_2[0][4] = ve_2[1][3]; //face5
ve_2[1][4] = iterTe_1[4][1]/4 + (qt_2[4]+qt_2[10]+qt_2[8])/12 +        ((iterTe_1[4][1]+iterTe_1[4][2])/2+(iterTe_1[4][1]+iterTe_1[10][2])/2+(iterTe_1[4][1]+iterTe_1[8][3])/2)/6;
ve_2[2][4] = iterTe_1[4][2]/4 + (qt_2[4]+qt_2[5]+qt_2[7]+qt_2[8])/16 + ((iterTe_1[4][2]+iterTe_1[4][3])/2+(iterTe_1[4][2]+iterTe_1[5][2])/2+(iterTe_1[4][2]+iterTe_1[8][2])/2+(iterTe_1[4][2]+iterTe_1[7][1])/2)/8;
ve_2[3][4] = ve_2[2][3];

ve_2[0][5] = ve_2[2][3]; //face6
ve_2[1][5] = ve_2[2][4];
ve_2[2][5] = ve_2[2][2];
ve_2[3][5] = ve_2[3][3];

ve_2[0][6] = ve_2[0][0]; //face7
ve_2[1][6] = ve_2[3][0];
ve_2[2][6] = iterTe_1[6][2]/4 + (qt_2[6]+qt_2[7] +qt_2[8])/12 +  ((iterTe_1[6][2]+iterTe_1[6][3])/2+(iterTe_1[6][2]+iterTe_1[7][0])/2 +(iterTe_1[6][2]+iterTe_1[8][1])/2)/6;
ve_2[3][6] = iterTe_1[6][3]/4 + (qt_2[6]+qt_2[8]+qt_2[9]+qt_2[10])/16 + ((iterTe_1[6][3]+iterTe_1[6][0])/2+(iterTe_1[6][3]+iterTe_1[8][0])/2+(iterTe_1[6][3]+iterTe_1[10][1])/2+(iterTe_1[6][3]+iterTe_1[9][2])/2)/8;

ve_2[0][7] = ve_2[1][6]; //face8
ve_2[1][7] = ve_2[2][2];
ve_2[2][7] = ve_2[2][4];
ve_2[3][7] = ve_2[2][6];

ve_2[0][8] = ve_2[2][6]; //face9
ve_2[1][8] = ve_2[2][7];
ve_2[2][8] = ve_2[1][4];
ve_2[3][8] = ve_2[3][6];

ve_2[0][9] = ve_2[0][6]; //face10
ve_2[1][9] = ve_2[3][6];
ve_2[2][9] = iterTe_1[9][2]/4 + (qt_2[9]+qt_2[10] +qt_2[11])/12 +  ((iterTe_1[9][2]+iterTe_1[9][3])/2+(iterTe_1[9][2]+iterTe_1[10][0])/2 +(iterTe_1[9][2]+iterTe_1[11][1])/2)/6;
ve_2[3][9] = ve_2[1][0];

ve_2[0][10] = ve_2[1][9]; //face11
ve_2[1][10] = ve_2[2][8];
ve_2[2][10] = ve_2[0][4];
ve_2[3][10] = ve_2[2][9];

ve_2[0][11] = ve_2[2][9]; //face12
ve_2[1][11] = ve_2[2][10];
ve_2[2][11] = ve_2[0][3];
ve_2[3][11] = ve_2[3][9];
}

void tetraedroIter3(void)
{
      //pontos nas faces
 for (int j = 0; j <48; j++)
 {
    qt_3[j] = (iterTe_2[j][0] + iterTe_2[j][1] + iterTe_2[j][2] + iterTe_2[j][3])/4;
 }

 //pontos nas linhas de intersecção
e_3[0][0] = (qt_3[0]+qt_3[36])/4 + (iterTe_2[0][0]+iterTe_2[0][1])/4; //face 1 (de 48)
e_3[1][0] = (qt_3[0]+qt_3[1])/4  + (iterTe_2[0][1]+iterTe_2[0][2])/4;
e_3[2][0] = (qt_3[0]+qt_3[3])/4  + (iterTe_2[0][2]+iterTe_2[0][3])/4;
e_3[3][0] = (qt_3[0]+qt_3[24])/4 + (iterTe_2[0][3]+iterTe_2[0][0])/4;

e_3[0][1] = (qt_3[1]+qt_3[39])/4 + (iterTe_2[1][0]+iterTe_2[1][1])/4; //face 2 (de 48)
e_3[1][1] = (qt_3[1]+qt_3[4])/4  + (iterTe_2[1][1]+iterTe_2[1][2])/4;
e_3[2][1] = (qt_3[1]+qt_3[2])/4  + (iterTe_2[1][2]+iterTe_2[1][3])/4;
e_3[3][1] = (qt_3[1]+qt_3[0])/4  + (iterTe_2[1][3]+iterTe_2[1][0])/4;

e_3[0][2] = (qt_3[2]+qt_3[1])/4 + (iterTe_2[2][0]+iterTe_2[2][1])/4; //face 3 (de 48)
e_3[1][2] = (qt_3[2]+qt_3[7])/4 + (iterTe_2[2][1]+iterTe_2[2][2])/4;
e_3[2][2] = (qt_3[2]+qt_3[8])/4 + (iterTe_2[2][2]+iterTe_2[2][3])/4;
e_3[3][2] = (qt_3[2]+qt_3[3])/4 + (iterTe_2[2][3]+iterTe_2[2][0])/4;

e_3[0][3] = (qt_3[3]+qt_3[0])/4 + (iterTe_2[3][0]+iterTe_2[3][1])/4; //face 4 (de 48)
e_3[1][3] = (qt_3[3]+qt_3[2])/4  + (iterTe_2[3][1]+iterTe_2[3][2])/4;
e_3[2][3] = (qt_3[3]+qt_3[11])/4  + (iterTe_2[3][2]+iterTe_2[3][3])/4;
e_3[3][3] = (qt_3[3]+qt_3[25])/4  + (iterTe_2[3][3]+iterTe_2[3][0])/4;

e_3[0][4] = (qt_3[4]+qt_3[47])/4 + (iterTe_2[4][0]+iterTe_2[4][1])/4; //face 5 (de 48)
e_3[1][4] = (qt_3[4]+qt_3[5])/4  + (iterTe_2[4][1]+iterTe_2[4][2])/4;
e_3[2][4] = (qt_3[4]+qt_3[7])/4  + (iterTe_2[4][2]+iterTe_2[4][3])/4;
e_3[3][4] = (qt_3[4]+qt_3[1])/4  + (iterTe_2[4][3]+iterTe_2[4][0])/4;

e_3[0][5] = (qt_3[5]+qt_3[46])/4 + (iterTe_2[5][0]+iterTe_2[5][1])/4; //face 6 (de 48)
e_3[1][5] = (qt_3[5]+qt_3[12])/4 + (iterTe_2[5][1]+iterTe_2[5][2])/4;
e_3[2][5] = (qt_3[5]+qt_3[6])/4  + (iterTe_2[5][2]+iterTe_2[5][3])/4;
e_3[3][5] = (qt_3[5]+qt_3[4])/4  + (iterTe_2[5][3]+iterTe_2[5][0])/4;

e_3[0][6] = (qt_3[6]+qt_3[5])/4  + (iterTe_2[6][0]+iterTe_2[6][1])/4; //face 7 (de 48)
e_3[1][6] = (qt_3[6]+qt_3[15])/4 + (iterTe_2[6][1]+iterTe_2[6][2])/4;
e_3[2][6] = (qt_3[6]+qt_3[9])/4  + (iterTe_2[6][2]+iterTe_2[6][3])/4;
e_3[3][6] = (qt_3[6]+qt_3[7])/4  + (iterTe_2[6][3]+iterTe_2[6][0])/4;

e_3[0][7] = (qt_3[7]+qt_3[4])/4 + (iterTe_2[7][0]+iterTe_2[7][1])/4; //face 8 (de 48)
e_3[1][7] = (qt_3[7]+qt_3[6])/4 + (iterTe_2[7][1]+iterTe_2[7][2])/4;
e_3[2][7] = (qt_3[7]+qt_3[8])/4 + (iterTe_2[7][2]+iterTe_2[7][3])/4;
e_3[3][7] = (qt_3[7]+qt_3[2])/4 + (iterTe_2[7][3]+iterTe_2[7][0])/4;

e_3[0][8] = (qt_3[8]+qt_3[7])/4  + (iterTe_2[8][0]+iterTe_2[8][1])/4; //face 9 (de 48)
e_3[1][8] = (qt_3[8]+qt_3[9])/4  + (iterTe_2[8][1]+iterTe_2[8][2])/4;
e_3[2][8] = (qt_3[8]+qt_3[11])/4  + (iterTe_2[8][2]+iterTe_2[8][3])/4;
e_3[3][8] = (qt_3[8]+qt_3[2])/4 + (iterTe_2[8][3]+iterTe_2[8][0])/4;

e_3[0][9] = (qt_3[9]+qt_3[6])/4  + (iterTe_2[9][0]+iterTe_2[9][1])/4; //face 10 (de 48)
e_3[1][9] = (qt_3[9]+qt_3[23])/4 + (iterTe_2[9][1]+iterTe_2[9][2])/4;
e_3[2][9] = (qt_3[9]+qt_3[10])/4 + (iterTe_2[9][2]+iterTe_2[9][3])/4;
e_3[3][9] = (qt_3[9]+qt_3[8])/4  + (iterTe_2[9][3]+iterTe_2[9][0])/4;

e_3[0][10] = (qt_3[10]+qt_3[9])/4  + (iterTe_2[10][0]+iterTe_2[10][1])/4; //face 11 (de 48)
e_3[1][10] = (qt_3[10]+qt_3[22])/4 + (iterTe_2[10][1]+iterTe_2[10][2])/4;
e_3[2][10] = (qt_3[10]+qt_3[29])/4 + (iterTe_2[10][2]+iterTe_2[10][3])/4;
e_3[3][10] = (qt_3[10]+qt_3[11])/4 + (iterTe_2[10][3]+iterTe_2[10][0])/4;

e_3[0][11] = (qt_3[11]+qt_3[8])/4  + (iterTe_2[11][0]+iterTe_2[11][1])/4; //face 12 (de 48)
e_3[1][11] = (qt_3[11]+qt_3[10])/4 + (iterTe_2[11][1]+iterTe_2[11][2])/4;
e_3[2][11] = (qt_3[11]+qt_3[28])/4 + (iterTe_2[11][2]+iterTe_2[11][3])/4;
e_3[3][11] = (qt_3[11]+qt_3[3])/4  + (iterTe_2[11][3]+iterTe_2[11][0])/4;

e_3[0][12] = (qt_3[12]+qt_3[46])/4 + (iterTe_2[12][0]+iterTe_2[12][1])/4; //face 13 (de 48)
e_3[1][12] = (qt_3[12]+qt_3[13])/4 + (iterTe_2[12][1]+iterTe_2[12][2])/4;
e_3[2][12] = (qt_3[12]+qt_3[15])/4 + (iterTe_2[12][2]+iterTe_2[12][3])/4;
e_3[3][12] = (qt_3[12]+qt_3[5])/4  + (iterTe_2[12][3]+iterTe_2[12][0])/4;

e_3[0][13] = (qt_3[13]+qt_3[45])/4 + (iterTe_2[13][0]+iterTe_2[13][1])/4; //face 14 (de 48)
e_3[1][13] = (qt_3[13]+qt_3[16])/4 + (iterTe_2[13][1]+iterTe_2[13][2])/4;
e_3[2][13] = (qt_3[13]+qt_3[14])/4 + (iterTe_2[13][2]+iterTe_2[13][3])/4;
e_3[3][13] = (qt_3[13]+qt_3[12])/4 + (iterTe_2[13][3]+iterTe_2[13][0])/4;

e_3[0][14] = (qt_3[14]+qt_3[13])/4 + (iterTe_2[14][0]+iterTe_2[14][1])/4; //face 15 (de 48)
e_3[1][14] = (qt_3[14]+qt_3[19])/4 + (iterTe_2[14][1]+iterTe_2[14][2])/4;
e_3[2][14] = (qt_3[14]+qt_3[20])/4 + (iterTe_2[14][2]+iterTe_2[14][3])/4;
e_3[3][14] = (qt_3[14]+qt_3[15])/4 + (iterTe_2[14][3]+iterTe_2[14][0])/4;

e_3[0][15] = (qt_3[15]+qt_3[12])/4  + (iterTe_2[15][0]+iterTe_2[15][1])/4; //face 16 (de 48)
e_3[1][15] = (qt_3[15]+qt_3[14])/4  + (iterTe_2[15][1]+iterTe_2[15][2])/4;
e_3[2][15] = (qt_3[15]+qt_3[23])/4 + (iterTe_2[15][2]+iterTe_2[15][3])/4;
e_3[3][15] = (qt_3[15]+qt_3[6])/4 + (iterTe_2[15][3]+iterTe_2[15][0])/4;

e_3[0][16] = (qt_3[16]+qt_3[42])/4 + (iterTe_2[16][0]+iterTe_2[16][1])/4; //face 17 (de 48)
e_3[1][16] = (qt_3[16]+qt_3[17])/4  + (iterTe_2[16][1]+iterTe_2[16][2])/4;
e_3[2][16] = (qt_3[16]+qt_3[19])/4  + (iterTe_2[16][2]+iterTe_2[16][3])/4;
e_3[3][16] = (qt_3[16]+qt_3[13])/4  + (iterTe_2[16][3]+iterTe_2[16][0])/4;

e_3[0][17] = (qt_3[17]+qt_3[41])/4 + (iterTe_2[17][0]+iterTe_2[17][1])/4; //face 18 (de 48)
e_3[1][17] = (qt_3[17]+qt_3[34])/4 + (iterTe_2[17][1]+iterTe_2[17][2])/4;
e_3[2][17] = (qt_3[17]+qt_3[18])/4  + (iterTe_2[17][2]+iterTe_2[17][3])/4;
e_3[3][17] = (qt_3[17]+qt_3[16])/4  + (iterTe_2[17][3]+iterTe_2[17][0])/4;

e_3[0][18] = (qt_3[18]+qt_3[17])/4  + (iterTe_2[18][0]+iterTe_2[18][1])/4; //face 19 (de 48)
e_3[1][18] = (qt_3[18]+qt_3[33])/4 + (iterTe_2[18][1]+iterTe_2[18][2])/4;
e_3[2][18] = (qt_3[18]+qt_3[21])/4  + (iterTe_2[18][2]+iterTe_2[18][3])/4;
e_3[3][18] = (qt_3[18]+qt_3[19])/4  + (iterTe_2[18][3]+iterTe_2[18][0])/4;

e_3[0][19] = (qt_3[19]+qt_3[16])/4 + (iterTe_2[19][0]+iterTe_2[19][1])/4; //face 20 (de 48)
e_3[1][19] = (qt_3[19]+qt_3[18])/4 + (iterTe_2[19][1]+iterTe_2[19][2])/4;
e_3[2][19] = (qt_3[19]+qt_3[20])/4 + (iterTe_2[19][2]+iterTe_2[19][3])/4;
e_3[3][19] = (qt_3[19]+qt_3[14])/4 + (iterTe_2[19][3]+iterTe_2[19][0])/4;

e_3[0][20] = (qt_3[20]+qt_3[19])/4 + (iterTe_2[20][0]+iterTe_2[20][1])/4; //face 21 (de 48)
e_3[1][20] = (qt_3[20]+qt_3[21])/4 + (iterTe_2[20][1]+iterTe_2[20][2])/4;
e_3[2][20] = (qt_3[20]+qt_3[23])/4 + (iterTe_2[20][2]+iterTe_2[20][3])/4;
e_3[3][20] = (qt_3[20]+qt_3[14])/4 + (iterTe_2[20][3]+iterTe_2[20][0])/4;

e_3[0][21] = (qt_3[21]+qt_3[18])/4  + (iterTe_2[21][0]+iterTe_2[21][1])/4; //face 22 (de 48)
e_3[1][21] = (qt_3[21]+qt_3[30])/4 + (iterTe_2[21][1]+iterTe_2[21][2])/4;
e_3[2][21] = (qt_3[21]+qt_3[22])/4 + (iterTe_2[21][2]+iterTe_2[21][3])/4;
e_3[3][21] = (qt_3[21]+qt_3[20])/4  + (iterTe_2[21][3]+iterTe_2[21][0])/4;

e_3[0][22] = (qt_3[22]+qt_3[21])/4  + (iterTe_2[22][0]+iterTe_2[22][1])/4; //face 23 (de 48)
e_3[1][22] = (qt_3[22]+qt_3[29])/4 + (iterTe_2[22][1]+iterTe_2[22][2])/4;
e_3[2][22] = (qt_3[22]+qt_3[10])/4 + (iterTe_2[22][2]+iterTe_2[22][3])/4;
e_3[3][22] = (qt_3[22]+qt_3[23])/4 + (iterTe_2[22][3]+iterTe_2[22][0])/4;

e_3[0][23] = (qt_3[23]+qt_3[20])/4 + (iterTe_2[23][0]+iterTe_2[23][1])/4; //face 24 (de 48)
e_3[1][23] = (qt_3[23]+qt_3[22])/4 + (iterTe_2[23][1]+iterTe_2[23][2])/4;
e_3[2][23] = (qt_3[23]+qt_3[9])/4  + (iterTe_2[23][2]+iterTe_2[23][3])/4;
e_3[3][23] = (qt_3[23]+qt_3[15])/4 + (iterTe_2[23][3]+iterTe_2[23][0])/4;

e_3[0][24] = (qt_3[24]+qt_3[0])/4 + (iterTe_2[24][0]+iterTe_2[24][1])/4; //face 25 (de 48)
e_3[1][24] = (qt_3[24]+qt_3[25])/4 + (iterTe_2[24][1]+iterTe_2[24][2])/4;
e_3[2][24] = (qt_3[24]+qt_3[27])/4 + (iterTe_2[24][2]+iterTe_2[24][3])/4;
e_3[3][24] = (qt_3[24]+qt_3[36])/4  + (iterTe_2[24][3]+iterTe_2[24][0])/4;

e_3[0][25] = (qt_3[25]+qt_3[3])/4 + (iterTe_2[25][0]+iterTe_2[25][1])/4; //face 26 (de 48)
e_3[1][25] = (qt_3[25]+qt_3[28])/4 + (iterTe_2[25][1]+iterTe_2[25][2])/4;
e_3[2][25] = (qt_3[25]+qt_3[26])/4 + (iterTe_2[25][2]+iterTe_2[25][3])/4;
e_3[3][25] = (qt_3[25]+qt_3[24])/4 + (iterTe_2[25][3]+iterTe_2[25][0])/4;

e_3[0][26] = (qt_3[26]+qt_3[25])/4 + (iterTe_2[26][0]+iterTe_2[26][1])/4; //face 27 (de 48)
e_3[1][26] = (qt_3[26]+qt_3[31])/4 + (iterTe_2[26][1]+iterTe_2[26][2])/4;
e_3[2][26] = (qt_3[26]+qt_3[32])/4 + (iterTe_2[26][2]+iterTe_2[26][3])/4;
e_3[3][26] = (qt_3[26]+qt_3[27])/4 + (iterTe_2[26][3]+iterTe_2[26][0])/4;

e_3[0][27] = (qt_3[27]+qt_3[24])/4 + (iterTe_2[27][0]+iterTe_2[27][1])/4; //face 28 (de 48)
e_3[1][27] = (qt_3[27]+qt_3[26])/4 + (iterTe_2[27][1]+iterTe_2[27][2])/4;
e_3[2][27] = (qt_3[27]+qt_3[35])/4 + (iterTe_2[27][2]+iterTe_2[27][3])/4;
e_3[3][27] = (qt_3[27]+qt_3[37])/4  + (iterTe_2[27][3]+iterTe_2[27][0])/4;

e_3[0][28] = (qt_3[28]+qt_3[11])/4 + (iterTe_2[28][0]+iterTe_2[28][1])/4; //face 29 (de 48)
e_3[1][28] = (qt_3[28]+qt_3[29])/4 + (iterTe_2[28][1]+iterTe_2[28][2])/4;
e_3[2][28] = (qt_3[28]+qt_3[31])/4 + (iterTe_2[28][2]+iterTe_2[28][3])/4;
e_3[3][28] = (qt_3[28]+qt_3[25])/4 + (iterTe_2[28][3]+iterTe_2[28][0])/4;

e_3[0][29] = (qt_3[29]+qt_3[10])/4 + (iterTe_2[29][0]+iterTe_2[29][1])/4; //face 30 (de 48)
e_3[1][29] = (qt_3[29]+qt_3[21])/4 + (iterTe_2[29][1]+iterTe_2[29][2])/4;
e_3[2][29] = (qt_3[29]+qt_3[30])/4 + (iterTe_2[29][2]+iterTe_2[29][3])/4;
e_3[3][29] = (qt_3[29]+qt_3[28])/4 + (iterTe_2[29][3]+iterTe_2[29][0])/4;

e_3[0][30] = (qt_3[30]+qt_3[29])/4 + (iterTe_2[30][0]+iterTe_2[30][1])/4; //face 31 (de 48)
e_3[1][30] = (qt_3[30]+qt_3[21])/4 + (iterTe_2[30][1]+iterTe_2[30][2])/4;
e_3[2][30] = (qt_3[30]+qt_3[33])/4 + (iterTe_2[30][2]+iterTe_2[30][3])/4;
e_3[3][30] = (qt_3[30]+qt_3[31])/4 + (iterTe_2[30][3]+iterTe_2[30][0])/4;

e_3[0][31] = (qt_3[31]+qt_3[28])/4 + (iterTe_2[31][0]+iterTe_2[31][1])/4; //face 32 (de 48)
e_3[1][31] = (qt_3[31]+qt_3[30])/4 + (iterTe_2[31][1]+iterTe_2[31][2])/4;
e_3[2][31] = (qt_3[31]+qt_3[32])/4 + (iterTe_2[31][2]+iterTe_2[31][3])/4;
e_3[3][31] = (qt_3[31]+qt_3[26])/4 + (iterTe_2[31][3]+iterTe_2[31][0])/4;

e_3[0][32] = (qt_3[32]+qt_3[31])/4 + (iterTe_2[32][0]+iterTe_2[32][1])/4; //face 33 (de 48)
e_3[1][32] = (qt_3[32]+qt_3[33])/4 + (iterTe_2[32][1]+iterTe_2[32][2])/4;
e_3[2][32] = (qt_3[32]+qt_3[35])/4 + (iterTe_2[32][2]+iterTe_2[32][3])/4;
e_3[3][32] = (qt_3[32]+qt_3[26])/4 + (iterTe_2[32][3]+iterTe_2[32][0])/4;

e_3[0][33] = (qt_3[33]+qt_3[30])/4 + (iterTe_2[33][0]+iterTe_2[33][1])/4; //face 34 (de 48)
e_3[1][33] = (qt_3[33]+qt_3[18])/4 + (iterTe_2[33][1]+iterTe_2[33][2])/4;
e_3[2][33] = (qt_3[33]+qt_3[34])/4 + (iterTe_2[33][2]+iterTe_2[33][3])/4;
e_3[3][33] = (qt_3[33]+qt_3[32])/4 + (iterTe_2[33][3]+iterTe_2[33][0])/4;

e_3[0][34] = (qt_3[34]+qt_3[33])/4 + (iterTe_2[34][0]+iterTe_2[34][1])/4; //face 35 (de 48)
e_3[1][34] = (qt_3[34]+qt_3[17])/4 + (iterTe_2[34][1]+iterTe_2[34][2])/4;
e_3[2][34] = (qt_3[34]+qt_3[41])/4 + (iterTe_2[34][2]+iterTe_2[34][3])/4;
e_3[3][34] = (qt_3[34]+qt_3[35])/4 + (iterTe_2[34][3]+iterTe_2[34][0])/4;

e_3[0][35] = (qt_3[35]+qt_3[32])/4 + (iterTe_2[35][0]+iterTe_2[35][1])/4; //face 36 (de 48)
e_3[1][35] = (qt_3[35]+qt_3[34])/4 + (iterTe_2[35][1]+iterTe_2[35][2])/4;
e_3[2][35] = (qt_3[35]+qt_3[40])/4  + (iterTe_2[35][2]+iterTe_2[35][3])/4;
e_3[3][35] = (qt_3[35]+qt_3[27])/4 + (iterTe_2[35][3]+iterTe_2[35][0])/4;

e_3[0][36] = (qt_3[36]+qt_3[24])/4 + (iterTe_2[36][0]+iterTe_2[36][1])/4; //face 37 (de 48)
e_3[1][36] = (qt_3[36]+qt_3[37])/4  + (iterTe_2[36][1]+iterTe_2[36][2])/4;
e_3[2][36] = (qt_3[36]+qt_3[39])/4  + (iterTe_2[36][2]+iterTe_2[36][3])/4;
e_3[3][36] = (qt_3[36]+qt_3[0])/4 + (iterTe_2[36][3]+iterTe_2[36][0])/4;

e_3[0][37] = (qt_3[37]+qt_3[27])/4 + (iterTe_2[37][0]+iterTe_2[37][1])/4; //face 38 (de 48)
e_3[1][37] = (qt_3[37]+qt_3[40])/4  + (iterTe_2[37][1]+iterTe_2[37][2])/4;
e_3[2][37] = (qt_3[37]+qt_3[38])/4  + (iterTe_2[37][2]+iterTe_2[37][3])/4;
e_3[3][37] = (qt_3[37]+qt_3[36])/4  + (iterTe_2[37][3]+iterTe_2[37][0])/4;

e_3[0][38] = (qt_3[38]+qt_3[37])/4 + (iterTe_2[38][0]+iterTe_2[38][1])/4; //face 39 (de 48)
e_3[1][38] = (qt_3[38]+qt_3[43])/4 + (iterTe_2[38][1]+iterTe_2[38][2])/4;
e_3[2][38] = (qt_3[38]+qt_3[44])/4 + (iterTe_2[38][2]+iterTe_2[38][3])/4;
e_3[3][38] = (qt_3[38]+qt_3[39])/4 + (iterTe_2[38][3]+iterTe_2[38][0])/4;

e_3[0][39] = (qt_3[39]+qt_3[36])/4 + (iterTe_2[39][0]+iterTe_2[39][1])/4; //face 40 (de 48)
e_3[1][39] = (qt_3[39]+qt_3[38])/4  + (iterTe_2[39][1]+iterTe_2[39][2])/4;
e_3[2][39] = (qt_3[39]+qt_3[47])/4  + (iterTe_2[39][2]+iterTe_2[39][3])/4;
e_3[3][39] = (qt_3[39]+qt_3[1])/4  + (iterTe_2[39][3]+iterTe_2[39][0])/4;

e_3[0][40] = (qt_3[40]+qt_3[35])/4 + (iterTe_2[40][0]+iterTe_2[40][1])/4; //face 41 (de 48)
e_3[1][40] = (qt_3[40]+qt_3[41])/4  + (iterTe_2[40][1]+iterTe_2[40][2])/4;
e_3[2][40] = (qt_3[40]+qt_3[43])/4  + (iterTe_2[40][2]+iterTe_2[40][3])/4;
e_3[3][40] = (qt_3[40]+qt_3[37])/4  + (iterTe_2[40][3]+iterTe_2[40][0])/4;

e_3[0][41] = (qt_3[41]+qt_3[34])/4 + (iterTe_2[41][0]+iterTe_2[41][1])/4; //face 42 (de 48)
e_3[1][41] = (qt_3[41]+qt_3[17])/4 + (iterTe_2[41][1]+iterTe_2[41][2])/4;
e_3[2][41] = (qt_3[41]+qt_3[42])/4  + (iterTe_2[41][2]+iterTe_2[41][3])/4;
e_3[3][41] = (qt_3[41]+qt_3[40])/4  + (iterTe_2[41][3]+iterTe_2[41][0])/4;

e_3[0][42] = (qt_3[42]+qt_3[41])/4  + (iterTe_2[42][0]+iterTe_2[42][1])/4; //face 43 (de 48)
e_3[1][42] = (qt_3[42]+qt_3[16])/4 + (iterTe_2[42][1]+iterTe_2[42][2])/4;
e_3[2][42] = (qt_3[42]+qt_3[45])/4  + (iterTe_2[42][2]+iterTe_2[42][3])/4;
e_3[3][42] = (qt_3[42]+qt_3[43])/4  + (iterTe_2[42][3]+iterTe_2[42][0])/4;

e_3[0][43] = (qt_3[43]+qt_3[40])/4 + (iterTe_2[43][0]+iterTe_2[43][1])/4; //face 44 (de 48)
e_3[1][43] = (qt_3[43]+qt_3[42])/4 + (iterTe_2[43][1]+iterTe_2[43][2])/4;
e_3[2][43] = (qt_3[43]+qt_3[44])/4 + (iterTe_2[43][2]+iterTe_2[43][3])/4;
e_3[3][43] = (qt_3[43]+qt_3[38])/4 + (iterTe_2[43][3]+iterTe_2[43][0])/4;

e_3[0][44] = (qt_3[44]+qt_3[43])/4  + (iterTe_2[44][0]+iterTe_2[44][1])/4; //face 45 (de 48)
e_3[1][44] = (qt_3[44]+qt_3[45])/4  + (iterTe_2[44][1]+iterTe_2[44][2])/4;
e_3[2][44] = (qt_3[44]+qt_3[47])/4  + (iterTe_2[44][2]+iterTe_2[44][3])/4;
e_3[3][44] = (qt_3[44]+qt_3[38])/4 + (iterTe_2[44][3]+iterTe_2[44][0])/4;

e_3[0][45] = (qt_3[45]+qt_3[42])/4  + (iterTe_2[45][0]+iterTe_2[45][1])/4; //face 46 (de 48)
e_3[1][45] = (qt_3[45]+qt_3[13])/4 + (iterTe_2[45][1]+iterTe_2[45][2])/4;
e_3[2][45] = (qt_3[45]+qt_3[46])/4 + (iterTe_2[45][2]+iterTe_2[45][3])/4;
e_3[3][45] = (qt_3[45]+qt_3[44])/4  + (iterTe_2[45][3]+iterTe_2[45][0])/4;

e_3[0][46] = (qt_3[46]+qt_3[45])/4  + (iterTe_2[46][0]+iterTe_2[46][1])/4; //face 47 (de 48)
e_3[1][46] = (qt_3[46]+qt_3[12])/4 + (iterTe_2[46][1]+iterTe_2[46][2])/4;
e_3[2][46] = (qt_3[46]+qt_3[5])/4 + (iterTe_2[46][2]+iterTe_2[46][3])/4;
e_3[3][46] = (qt_3[46]+qt_3[47])/4 + (iterTe_2[46][3]+iterTe_2[46][0])/4;

e_3[0][47] = (qt_3[47]+qt_3[44])/4  + (iterTe_2[47][0]+iterTe_2[47][1])/4; //face 48 (de 48)
e_3[1][47] = (qt_3[47]+qt_3[46])/4 + (iterTe_2[47][1]+iterTe_2[47][2])/4;
e_3[2][47] = (qt_3[47]+qt_3[4])/4 + (iterTe_2[47][2]+iterTe_2[47][3])/4;
e_3[3][47] = (qt_3[47]+qt_3[39])/4  + (iterTe_2[47][3]+iterTe_2[47][0])/4;

 //pontos nos vertices quese interceptam
ve_3[0][0] = iterTe_2[0][0]/4 + (qt_3[0]+qt_3[24]+qt_3[36])/12          + ((iterTe_2[0][0]+iterTe_2[0][1])/2+(iterTe_2[0][0]+iterTe_2[24][1])/2+(iterTe_2[0][0]+iterTe_2[36][1])/2)/6; //face1
ve_3[1][0] = iterTe_2[0][1]/4 + (qt_3[0]+qt_3[36]+qt_3[39]+qt_3[1])/16  + ((iterTe_2[0][1]+iterTe_2[0][2])/2+(iterTe_2[0][1]+iterTe_2[36][0])/2+(iterTe_2[0][1]+iterTe_2[39][1])/2+(iterTe_2[0][1]+iterTe_2[1][1])/2)/8;
ve_3[2][0] = iterTe_2[0][2]/4 + (qt_3[0]+qt_3[1] +qt_3[2]+qt_3[3])/16   + ((iterTe_2[0][2]+iterTe_2[0][3])/2+(iterTe_2[0][2]+iterTe_2[1][0])/2 +(iterTe_2[0][2]+iterTe_2[2][1])/2+(iterTe_2[0][2]+iterTe_2[3][2])/2)/8;
ve_3[3][0] = iterTe_2[0][3]/4 + (qt_3[0]+qt_3[3] +qt_3[25]+qt_3[24])/16 + ((iterTe_2[0][3]+iterTe_2[0][0])/2+(iterTe_2[0][3]+iterTe_2[3][1])/2 +(iterTe_2[0][3]+iterTe_2[25][1])/2+(iterTe_2[0][3]+iterTe_2[24][2])/2)/8;

ve_3[0][1] = ve_3[1][0]; //face2
ve_3[1][1] = iterTe_2[1][1]/4 + (qt_3[1]+qt_3[39]+qt_3[47]+qt_3[4])/16 + ((iterTe_2[1][1]+iterTe_2[1][2])/2+(iterTe_2[1][1]+iterTe_2[39][1])/2+(iterTe_2[1][1]+iterTe_2[47][2])/2+(iterTe_2[1][2]+iterTe_2[4][1])/2)/8;
ve_3[2][1] = iterTe_2[1][2]/4 + (qt_3[1]+qt_3[4]+qt_3[7]+qt_3[2])/16  + ((iterTe_2[1][2]+iterTe_2[1][3])/2+(iterTe_2[1][2]+iterTe_2[4][0])/2  +(iterTe_2[1][2]+iterTe_2[7][1])/2 +(iterTe_2[1][2]+iterTe_2[2][2])/2)/8;
ve_3[3][1] = ve_3[2][0];

ve_3[0][2] = ve_3[2][0]; //face3
ve_3[1][2] = ve_3[2][1];
ve_3[2][2] = iterTe_2[2][2]/4 + (qt_3[2]+qt_3[7]+qt_3[8])/12  + ((iterTe_2[2][2]+iterTe_2[2][3])/2+(iterTe_2[2][2]+iterTe_2[7][0])/2  +(iterTe_2[2][2]+iterTe_2[8][1])/2)/6;
ve_3[3][2] = iterTe_2[3][2]/4 + (qt_3[2]+qt_3[8]+qt_3[11]+qt_3[3])/16  + ((iterTe_2[2][3]+iterTe_2[2][0])/2+(iterTe_2[2][3]+iterTe_2[8][0])/2  +(iterTe_2[2][3]+iterTe_2[11][1])/2 +(iterTe_2[2][3]+iterTe_2[3][3])/2)/8;

ve_3[0][3] = ve_3[3][0]; //face4
ve_3[1][3] = ve_3[0][2];
ve_3[2][3] = ve_3[3][2];
ve_3[3][3] = iterTe_2[3][3]/4 + (qt_3[3]+qt_3[11]+qt_3[28]+qt_3[25])/16  + ((iterTe_2[3][3]+iterTe_2[3][0])/2+(iterTe_2[3][3]+iterTe_2[11][0])/2  +(iterTe_2[3][3]+iterTe_2[28][1])/2 +(iterTe_2[3][3]+iterTe_2[25][2])/2)/8;

ve_3[0][4] = ve_3[1][1]; //face5
ve_3[1][4] = iterTe_2[4][1]/4 + (qt_3[4]+qt_3[47]+qt_3[46]+qt_3[5])/16  + ((iterTe_2[4][1]+iterTe_2[4][2])/2+(iterTe_2[4][1]+iterTe_2[47][1])/2+(iterTe_2[4][1]+iterTe_2[46][2])/2+(iterTe_2[4][1]+iterTe_2[5][1])/2)/8;
ve_3[2][4] = iterTe_2[4][2]/4 + (qt_3[4]+qt_3[5] +qt_3[6] +qt_3[7])/16  + ((iterTe_2[4][2]+iterTe_2[4][3])/2+(iterTe_2[4][2]+iterTe_2[5][0])/2 +(iterTe_2[4][2]+iterTe_2[6][1])/2+(iterTe_2[4][2]+iterTe_2[7][2])/2)/8;
ve_3[3][4] = ve_3[2][1];

ve_3[0][5] = ve_3[1][4]; //face6
ve_3[1][5] = iterTe_2[5][1]/4 + (qt_3[5]+qt_3[46]+qt_3[12])/12          + ((iterTe_2[5][1]+iterTe_2[5][2])/2+(iterTe_2[5][1]+iterTe_2[46][1])/2+(iterTe_2[5][1]+iterTe_2[12][1])/2)/6;
ve_3[2][5] = iterTe_2[5][2]/4 + (qt_3[5]+qt_3[12]+qt_3[15]+qt_3[6])/16  + ((iterTe_2[5][2]+iterTe_2[5][3])/2+(iterTe_2[5][2]+iterTe_2[12][0])/2  +(iterTe_2[5][2]+iterTe_2[15][1])/2 +(iterTe_2[5][2]+iterTe_2[6][2])/2)/8;
ve_3[3][5] = ve_3[2][4];

ve_3[0][6] = ve_3[3][5]; //face7
ve_3[1][6] = ve_3[2][5];
ve_3[2][6] = iterTe_2[6][2]/4 + (qt_3[6]+qt_3[15]+qt_3[23]+qt_3[9])/16  + ((iterTe_2[6][2]+iterTe_2[6][3])/2+(iterTe_2[6][2]+iterTe_2[15][0])/2  +(iterTe_2[6][2]+iterTe_2[23][0])/2 +(iterTe_2[6][2]+iterTe_2[9][2])/2)/8;
ve_3[3][6] = iterTe_2[6][3]/4 + (qt_3[6]+qt_3[9]+qt_3[8]+qt_3[7])/16  + ((iterTe_2[6][3]+iterTe_2[6][0])/2+(iterTe_2[6][3]+iterTe_2[9][1])/2  +(iterTe_2[6][3]+iterTe_2[8][2])/2 +(iterTe_2[6][3]+iterTe_2[7][2])/2)/8;

ve_3[0][7] = ve_3[3][4]; //face8
ve_3[1][7] = ve_3[3][5];
ve_3[2][7] = ve_3[3][6];
ve_3[3][7] = ve_3[2][2];
  
ve_3[0][8] = ve_3[3][7]; //face9
ve_3[1][8] = ve_3[2][7];
ve_3[2][8] = iterTe_2[8][2]/4 + (qt_3[8]+qt_3[9] +qt_3[10] +qt_3[11])/16  + ((iterTe_2[8][2]+iterTe_2[8][3])/2+(iterTe_2[8][2]+iterTe_2[9][0])/2 +(iterTe_2[8][2]+iterTe_2[10][1])/2+(iterTe_2[8][2]+iterTe_2[11][2])/2)/8;
ve_3[3][8] = ve_3[3][2];

ve_3[0][9] = ve_3[1][8]; //face10
ve_3[1][9] = ve_3[2][6];
ve_3[2][9] = iterTe_2[9][2]/4 + (qt_3[9]+qt_3[23]+qt_3[22]+qt_3[10])/16  + ((iterTe_2[9][2]+iterTe_2[9][3])/2+(iterTe_2[9][2]+iterTe_2[23][3])/2  +(iterTe_2[9][2]+iterTe_2[22][0])/2 +(iterTe_2[9][2]+iterTe_2[10][2])/2)/8;
ve_3[3][9] = ve_3[2][8];

ve_3[0][10] = ve_3[3][9]; //face11
ve_3[1][10] = ve_3[2][9];
ve_3[2][10] = iterTe_2[10][2]/4 + (qt_3[10]+qt_3[22]+qt_3[29])/12          + ((iterTe_2[10][2]+iterTe_2[10][3])/2+(iterTe_2[10][2]+iterTe_2[22][3])/2  +(iterTe_2[10][2]+iterTe_2[29][2])/2)/6;
ve_3[3][10] = iterTe_2[10][3]/4 + (qt_3[10]+qt_3[29]+qt_3[28]+qt_3[11])/16 + ((iterTe_2[10][3]+iterTe_2[10][0])/2+(iterTe_2[10][3]+iterTe_2[29][1])/2  +(iterTe_2[10][3]+iterTe_2[28][2])/2 +(iterTe_2[10][3]+iterTe_2[11][3])/2)/8;

ve_3[0][11] = ve_3[2][3]; //face12
ve_3[1][11] = ve_3[0][10];
ve_3[2][11] = ve_3[3][10];
ve_3[3][11] = ve_3[3][3];

ve_3[0][12] = ve_3[1][5]; //face13
ve_3[1][12] = iterTe_2[12][1]/4 + (qt_3[12]+qt_3[46] +qt_3[45] +qt_3[13])/16  + ((iterTe_2[12][1]+iterTe_2[12][2])/2+(iterTe_2[12][1]+iterTe_2[46][2])/2 +(iterTe_2[12][1]+iterTe_2[45][3])/2+(iterTe_2[12][1]+iterTe_2[13][1])/2)/8;
ve_3[2][12] = iterTe_2[12][2]/4 + (qt_3[12]+qt_3[13] +qt_3[14] +qt_3[15])/16  + ((iterTe_2[12][2]+iterTe_2[12][3])/2+(iterTe_2[12][2]+iterTe_2[13][0])/2 +(iterTe_2[12][2]+iterTe_2[14][1])/2+(iterTe_2[12][2]+iterTe_2[15][2])/2)/8;
ve_3[3][12] = ve_3[2][5];

ve_3[0][13] = ve_3[1][12]; //face14
ve_3[1][13] = iterTe_2[13][1]/4 + (qt_3[13]+qt_3[45]+qt_3[42]+qt_3[16])/16  + ((iterTe_2[13][1]+iterTe_2[13][2])/2+(iterTe_2[13][1]+iterTe_2[45][2])/2  +(iterTe_2[13][1]+iterTe_2[42][3])/2 +(iterTe_2[13][1]+iterTe_2[16][1])/2)/8;
ve_3[2][13] = iterTe_2[13][2]/4 + (qt_3[13]+qt_3[16]+qt_3[19]+qt_3[14])/16  + ((iterTe_2[13][2]+iterTe_2[13][3])/2+(iterTe_2[13][2]+iterTe_2[16][0])/2  +(iterTe_2[13][2]+iterTe_2[19][1])/2 +(iterTe_2[13][2]+iterTe_2[14][2])/2)/8;
ve_3[3][13] = ve_3[2][12];

ve_3[0][14] = ve_3[3][13]; //face15
ve_3[1][14] = ve_3[2][13];
ve_3[2][14] = iterTe_2[14][2]/4 + (qt_3[14]+qt_3[19]+qt_3[20])/12          + ((iterTe_2[14][2]+iterTe_2[14][3])/2+(iterTe_2[14][2]+iterTe_2[19][0])/2  +(iterTe_2[14][2]+iterTe_2[20][1])/2)/6;
ve_3[3][14] = iterTe_2[14][3]/4 + (qt_3[14]+qt_3[20]+qt_3[23]+qt_3[15])/16 + ((iterTe_2[14][3]+iterTe_2[14][0])/2+(iterTe_2[14][3]+iterTe_2[20][0])/2  +(iterTe_2[14][3]+iterTe_2[23][1])/2 +(iterTe_2[14][3]+iterTe_2[15][3])/2)/8;

ve_3[0][15] = ve_3[3][12]; //face16
ve_3[1][15] = ve_3[2][12];
ve_3[2][15] = ve_3[3][14];
ve_3[3][15] = ve_3[2][6];

ve_3[0][16] = ve_3[1][13]; //face17
ve_3[1][16] = iterTe_2[16][1]/4 + (qt_3[16]+qt_3[42]+qt_3[41]+qt_3[17])/16  + ((iterTe_2[16][1]+iterTe_2[16][2])/2+(iterTe_2[16][1]+iterTe_2[42][2])/2+(iterTe_2[16][1]+iterTe_2[41][3])/2+(iterTe_2[16][1]+iterTe_2[17][1])/2)/8;
ve_3[2][16] = iterTe_2[16][2]/4 + (qt_3[16]+qt_3[17] +qt_3[18] +qt_3[19])/16  + ((iterTe_2[16][2]+iterTe_2[16][3])/2+(iterTe_2[16][2]+iterTe_2[17][0])/2 +(iterTe_2[16][2]+iterTe_2[18][1])/2+(iterTe_2[16][2]+iterTe_2[19][2])/2)/8;
ve_3[3][16] = ve_3[2][13];

ve_3[0][17] = ve_3[1][16]; //face18
ve_3[1][17] = iterTe_2[17][1]/4 + (qt_3[17]+qt_3[41]+qt_3[34])/12          + ((iterTe_2[17][1]+iterTe_2[17][2])/2+(iterTe_2[17][1]+iterTe_2[41][3])/2+(iterTe_2[17][1]+iterTe_2[34][3])/2)/6;
ve_3[2][17] = iterTe_2[17][2]/4 + (qt_3[17]+qt_3[34]+qt_3[33]+qt_3[18])/16  + ((iterTe_2[17][2]+iterTe_2[17][3])/2+(iterTe_2[17][2]+iterTe_2[34][2])/2  +(iterTe_2[17][2]+iterTe_2[33][3])/2 +(iterTe_2[18][2]+iterTe_2[6][2])/2)/8;
ve_3[3][17] = ve_3[2][16];

ve_3[0][18] = ve_3[3][17]; //face19
ve_3[1][18] = ve_3[2][17];
ve_3[2][18] = iterTe_2[18][2]/4 + (qt_3[18]+qt_3[33]+qt_3[30]+qt_3[21])/16  + ((iterTe_2[18][2]+iterTe_2[18][3])/2+(iterTe_2[18][2]+iterTe_2[33][1])/2  +(iterTe_2[18][2]+iterTe_2[30][3])/2 +(iterTe_2[18][2]+iterTe_2[21][2])/2)/8;
ve_3[3][18] = iterTe_2[18][3]/4 + (qt_3[18]+qt_3[21]+qt_3[20]+qt_3[19])/16  + ((iterTe_2[18][3]+iterTe_2[18][0])/2+(iterTe_2[18][3]+iterTe_2[21][1])/2  +(iterTe_2[18][3]+iterTe_2[20][2])/2 +(iterTe_2[18][3]+iterTe_2[19][3])/2)/8;

ve_3[0][19] = ve_3[3][16]; //face20
ve_3[1][19] = ve_3[3][17];
ve_3[2][19] = ve_3[3][18];
ve_3[3][19] = ve_3[2][14];

ve_3[0][20] = ve_3[2][14]; //face21
ve_3[1][20] = ve_3[2][19];
ve_3[2][20] = iterTe_2[20][2]/4 + (qt_3[20]+qt_3[21] +qt_3[22] +qt_3[23])/16  + ((iterTe_2[20][2]+iterTe_2[20][3])/2+(iterTe_2[20][2]+iterTe_2[21][0])/2 +(iterTe_2[20][2]+iterTe_2[22][1])/2+(iterTe_2[20][2]+iterTe_2[23][2])/2)/8;
ve_3[3][20] = ve_3[3][14];

ve_3[0][21] = ve_3[1][20]; //face22
ve_3[1][21] = ve_3[2][18];
ve_3[2][21] = iterTe_2[21][2]/4 + (qt_3[21]+qt_3[29]+qt_3[30]+qt_3[22])/16  + ((iterTe_2[21][2]+iterTe_2[21][3])/2+(iterTe_2[21][2]+iterTe_2[30][2])/2  +(iterTe_2[21][2]+iterTe_2[29][3])/2 +(iterTe_2[21][2]+iterTe_2[22][2])/2)/8;
ve_3[3][21] = ve_3[2][20];

ve_3[0][22] = ve_3[3][21]; //face23
ve_3[1][22] = ve_3[2][21];
ve_3[2][22] = ve_3[2][10];
ve_3[3][22] = ve_3[1][10];

ve_3[0][23] = ve_3[2][15]; //face24
ve_3[1][23] = ve_3[0][22];
ve_3[2][23] = ve_3[3][22];
ve_3[3][23] = ve_3[3][15];

ve_3[0][24] = ve_3[0][0]; //face25
ve_3[1][24] = ve_3[3][0];
ve_3[2][24] = iterTe_2[24][2]/4 + (qt_3[24]+qt_3[25] +qt_3[26] +qt_3[27])/16  + ((iterTe_2[24][2]+iterTe_2[24][3])/2+(iterTe_2[24][2]+iterTe_2[25][0])/2 +(iterTe_2[24][2]+iterTe_2[26][1])/2+(iterTe_2[24][2]+iterTe_2[27][2])/2)/8;
ve_3[3][24] = iterTe_2[24][3]/4 + (qt_3[24]+qt_3[27]+qt_3[37]+qt_3[36])/16 + ((iterTe_2[24][3]+iterTe_2[24][0])/2+(iterTe_2[24][3]+iterTe_2[27][1])/2  +(iterTe_2[24][3]+iterTe_2[37][1])/2 +(iterTe_2[24][3]+iterTe_2[36][2])/2)/8;

ve_3[0][25] = ve_3[1][24]; //face26
ve_3[1][25] = ve_3[3][3];
ve_3[2][25] = iterTe_2[25][2]/4 + (qt_3[25]+qt_3[28]+qt_3[31]+qt_3[26])/16  + ((iterTe_2[25][2]+iterTe_2[25][3])/2+(iterTe_2[25][2]+iterTe_2[28][0])/2  +(iterTe_2[25][2]+iterTe_2[31][1])/2 +(iterTe_2[25][2]+iterTe_2[26][2])/2)/8;
ve_3[3][25] = ve_3[2][24];

ve_3[0][26] = ve_3[2][24]; //face27
ve_3[1][26] = ve_3[2][25];
ve_3[2][26] = iterTe_2[26][2]/4 + (qt_3[26]+qt_3[31]+qt_3[32])/12          + ((iterTe_2[26][2]+iterTe_2[26][3])/2+(iterTe_2[26][2]+iterTe_2[31][0])/2  +(iterTe_2[26][2]+iterTe_2[32][1])/2)/6;
ve_3[3][26] = iterTe_2[26][3]/4 + (qt_3[26]+qt_3[32]+qt_3[35]+qt_3[27])/16 + ((iterTe_2[26][3]+iterTe_2[26][0])/2+(iterTe_2[26][3]+iterTe_2[32][0])/2  +(iterTe_2[26][3]+iterTe_2[35][1])/2 +(iterTe_2[26][3]+iterTe_2[27][3])/2)/8;

ve_3[0][27] = ve_3[3][24]; //face28
ve_3[1][27] = ve_3[2][24];
ve_3[2][27] = ve_3[3][26];
ve_3[3][27] = iterTe_2[27][3]/4 + (qt_3[27]+qt_3[35]+qt_3[40]+qt_3[37])/16 + ((iterTe_2[27][3]+iterTe_2[27][0])/2+(iterTe_2[27][3]+iterTe_2[35][0])/2  +(iterTe_2[27][3]+iterTe_2[40][1])/2 +(iterTe_2[27][3]+iterTe_2[37][2])/2)/8;

ve_3[0][28] = ve_3[1][25]; //face29
ve_3[1][28] = ve_3[2][11];
ve_3[2][28] = iterTe_2[28][2]/4 + (qt_3[28]+qt_3[29] +qt_3[30] +qt_3[31])/16  + ((iterTe_2[28][2]+iterTe_2[28][3])/2+(iterTe_2[28][2]+iterTe_2[29][0])/2 +(iterTe_2[28][2]+iterTe_2[30][1])/2+(iterTe_2[28][2]+iterTe_2[31][2])/2)/8;
ve_3[3][28] = ve_3[2][25];

ve_3[0][29] = ve_3[1][28]; //face30
ve_3[1][29] = ve_3[2][10];
ve_3[2][29] = ve_3[1][22];
ve_3[3][29] = ve_3[2][28];

ve_3[0][30] = ve_3[3][29]; //face31
ve_3[1][30] = ve_3[2][29];
ve_3[2][30] = ve_3[1][21];
ve_3[3][30] = iterTe_2[30][3]/4 + (qt_3[30]+qt_3[33]+qt_3[32]+qt_3[31])/16  + ((iterTe_2[30][3]+iterTe_2[30][0])/2+(iterTe_2[30][3]+iterTe_2[33][1])/2  +(iterTe_2[30][3]+iterTe_2[32][2])/2 +(iterTe_2[30][3]+iterTe_2[31][3])/2)/8;

ve_3[0][31] = ve_3[1][26]; //face32
ve_3[1][31] = ve_3[0][30];
ve_3[2][31] = ve_3[3][30];
ve_3[3][31] = ve_3[2][26];

ve_3[0][32] = ve_3[2][26]; //face33
ve_3[1][32] = ve_3[2][31];
ve_3[2][32] = iterTe_2[32][2]/4 + (qt_3[32]+qt_3[33] +qt_3[34] +qt_3[35])/16  + ((iterTe_2[32][2]+iterTe_2[32][3])/2+(iterTe_2[32][2]+iterTe_2[33][0])/2 +(iterTe_2[32][2]+iterTe_2[34][1])/2+(iterTe_2[32][2]+iterTe_2[35][2])/2)/8;
ve_3[3][32] = ve_3[3][26];

ve_3[0][33] = ve_3[1][32]; //face34
ve_3[1][33] = ve_3[2][30];
ve_3[2][33] = ve_3[1][18];
ve_3[3][33] = ve_3[2][32];

ve_3[0][34] = ve_3[3][33]; //face35
ve_3[1][34] = ve_3[2][33];
ve_3[2][34] = ve_3[1][17];
ve_3[3][34] = iterTe_2[34][3]/4 + (qt_3[34]+qt_3[41]+qt_3[40]+qt_3[35])/16  + ((iterTe_2[34][3]+iterTe_2[34][0])/2+(iterTe_2[34][3]+iterTe_2[41][1])/2  +(iterTe_2[34][3]+iterTe_2[40][2])/2 +(iterTe_2[34][3]+iterTe_2[35][3])/2)/8;

ve_3[0][35] = ve_3[2][27]; //face36
ve_3[1][35] = ve_3[0][34];
ve_3[2][35] = ve_3[3][34];
ve_3[3][35] = ve_3[3][27];

ve_3[0][36] = ve_3[0][0]; //face37
ve_3[1][36] = ve_3[3][24];
ve_3[2][36] = iterTe_2[36][2]/4 + (qt_3[36]+qt_3[37] +qt_3[38] +qt_3[39])/16  + ((iterTe_2[36][2]+iterTe_2[36][3])/2+(iterTe_2[36][2]+iterTe_2[37][0])/2 +(iterTe_2[36][2]+iterTe_2[38][1])/2+(iterTe_2[36][2]+iterTe_2[39][2])/2)/8;
ve_3[3][36] = ve_3[1][0];

ve_3[0][37] = ve_3[1][36]; //face38
ve_3[1][37] = ve_3[3][27];
ve_3[2][37] = iterTe_2[37][2]/4 + (qt_3[37]+qt_3[40]+qt_3[43]+qt_3[38])/16  + ((iterTe_2[37][2]+iterTe_2[37][3])/2+(iterTe_2[37][2]+iterTe_2[40][0])/2  +(iterTe_2[37][2]+iterTe_2[43][1])/2 +(iterTe_2[37][2]+iterTe_2[38][2])/2)/8;
ve_3[3][37] = ve_3[2][36];

ve_3[0][38] = ve_3[3][37]; //face39
ve_3[1][38] = ve_3[2][37];
ve_3[2][38] = iterTe_2[38][2]/4 + (qt_3[38]+qt_3[43]+qt_3[44])/12  + ((iterTe_2[38][2]+iterTe_2[38][3])/2+(iterTe_2[38][2]+iterTe_2[43][0])/2  +(iterTe_2[38][2]+iterTe_2[44][1])/2)/6;
ve_3[3][38] = iterTe_2[38][3]/4 + (qt_3[38]+qt_3[44]+qt_3[47]+qt_3[39])/16  + ((iterTe_2[38][3]+iterTe_2[38][0])/2+(iterTe_2[38][3]+iterTe_2[44][0])/2  +(iterTe_2[38][3]+iterTe_2[47][1])/2 +(iterTe_2[38][3]+iterTe_2[39][3])/2)/8;

ve_3[0][39] = ve_3[3][36]; //face40
ve_3[1][39] = ve_3[2][36];
ve_3[2][39] = ve_3[3][38];
ve_3[3][39] = ve_3[1][1];

ve_3[0][40] = ve_3[1][37]; //face41
ve_3[1][40] = ve_3[2][35];
ve_3[2][40] = iterTe_2[40][2]/4 + (qt_3[40]+qt_3[41] +qt_3[42] +qt_3[43])/16  + ((iterTe_2[40][2]+iterTe_2[40][3])/2+(iterTe_2[40][2]+iterTe_2[41][0])/2 +(iterTe_2[40][2]+iterTe_2[42][1])/2+(iterTe_2[40][2]+iterTe_2[43][2])/2)/8;
ve_3[3][40] = ve_3[2][37];

ve_3[0][41] = ve_3[1][40]; //face42
ve_3[1][41] = ve_3[2][34];
ve_3[2][41] = ve_3[0][17];
ve_3[3][41] = ve_3[2][40];

ve_3[0][42] = ve_3[3][41]; //face43
ve_3[1][42] = ve_3[2][41];
ve_3[2][42] = ve_3[0][16];
ve_3[3][42] = iterTe_2[42][3]/4 + (qt_3[42]+qt_3[43]+qt_3[45]+qt_3[44])/16 + ((iterTe_2[42][3]+iterTe_2[42][0])/2+(iterTe_2[42][3]+iterTe_2[45][1])/2  +(iterTe_2[42][3]+iterTe_2[44][2])/2 +(iterTe_2[42][3]+iterTe_2[43][3])/2)/8;

ve_3[0][43] = ve_3[3][40]; //face44
ve_3[1][43] = ve_3[2][40];
ve_3[2][43] = ve_3[3][42];
ve_3[3][43] = ve_3[2][38];

ve_3[0][44] = ve_3[3][43]; //face45
ve_3[1][44] = ve_3[2][43];
ve_3[2][44] = iterTe_2[44][2]/4 + (qt_3[44]+qt_3[45] +qt_3[46]+qt_3[47])/16   + ((iterTe_2[44][2]+iterTe_2[44][3])/2+(iterTe_2[44][2]+iterTe_2[45][0])/2 +(iterTe_2[44][2]+iterTe_2[46][1])/2+(iterTe_2[44][2]+iterTe_2[47][2])/2)/8;
ve_3[3][44] = ve_3[3][38];

ve_3[0][45] = ve_3[3][42]; //face46
ve_3[1][45] = ve_3[2][42];
ve_3[2][45] = ve_3[0][13];
ve_3[3][45] = ve_3[2][44];

ve_3[0][46] = ve_3[3][45]; //face47
ve_3[1][46] = ve_3[2][45];
ve_3[2][46] = ve_3[1][5];
ve_3[3][46] = ve_3[0][5];

ve_3[0][47] = ve_3[3][44]; //face48
ve_3[1][47] = ve_3[2][44];
ve_3[2][47] = ve_3[1][4];
ve_3[3][47] = ve_3[0][4];

}


void montaVetorTetra1(void)
{
     i=0;
    for(int c=0; c<4; c++)
    {
        iterTe_1[i][0]=ve[0][c];
        iterTe_1[i][1]=e[0][c];
        iterTe_1[i][2]=qt[c];
        iterTe_1[i][3]=e[2][c];
i++;
        iterTe_1[i][0]=e[0][c];
        iterTe_1[i][1]=ve[1][c];
        iterTe_1[i][2]=e[1][c];
        iterTe_1[i][3]=qt[c];
i++;
        iterTe_1[i][0]=qt[c];
        iterTe_1[i][1]=e[1][c];
        iterTe_1[i][2]=ve[2][c];
        iterTe_1[i][3]=e[2][c];
i++;
        }

}   

void montaVetorTetra2(void)
{
     i=0;
    for(int c=0; c<12; c++)
    {
iterTe_2[i][0] = ve_2[0][c]; 
iterTe_2[i][1] = e_2[0][c]; 
iterTe_2[i][2] = qt_2[c];
iterTe_2[i][3] = e_2[3][c];
 i++;
iterTe_2[i][0] = e_2[0][c];
iterTe_2[i][1] = ve_2[1][c];
iterTe_2[i][2] = e_2[1][c]; 
iterTe_2[i][3] = qt_2[c];
 i++;
iterTe_2[i][0] = qt_2[c];
iterTe_2[i][1] = e_2[1][c];
iterTe_2[i][2] = ve_2[2][c];
iterTe_2[i][3] = e_2[2][c];
 i++;
iterTe_2[i][0] = e_2[3][c];
iterTe_2[i][1] = qt_2[c];
iterTe_2[i][2] = e_2[2][c];
iterTe_2[i][3] = ve_2[3][c];
 i++;           
}       

}   


// Função de callback de desenho
void RenderScene(void)
{
	// Limpa a janela com a cor especificada como cor de fundo
	glClear(GL_COLOR_BUFFER_BIT);

    if (isFlat == 1) glShadeModel(GL_FLAT);
    else glShadeModel(GL_SMOOTH);

    tet = 4; tet1 = 4; tet2 = 12; tet3 = 48;
    
    hex = 6; hex1 = 6; hex2 = 24; hex3 = 96;
    
    // Chamadas de funções OpenGL para desenho
    if (whatIs != 1) {tet = 0;}
    if (whatIs != 6) {tet1 = 0;}
    if (whatIs != 7) {tet2 = 0;}
    if (whatIs != 8) {tet3 = 0;}
    if (whatIs != 2) {hex = 0;}
    if (whatIs != 3) {hex1 = 0;}
    if (whatIs != 4) {hex2 = 0;}
    if (whatIs != 5) {hex3 = 0;}

 //Tetraedro
if (isLine) glBegin(GL_LINE_LOOP);
else glBegin(GL_TRIANGLES);
 for(i=0;i<tet;i++)
 {
     glColor3f (1/te[i][0][0], 1/te[i][0][1], 1/te[i][0][2]);
     glVertex3f(te[i][0][0],te[i][0][1],te[i][0][2]);
     glColor3f (1/te[i][1][0], 1/te[i][1][1], 1/te[i][1][2]);
     glVertex3f(te[i][1][0],te[i][1][1],te[i][1][2]);
     glColor3f (1/te[i][2][0], 1/te[i][2][1], 1/te[i][2][2]);
     glVertex3f(te[i][2][0],te[i][2][1],te[i][2][2]);
 }
glEnd();
   
tetraedroIter1();   

   for(int c=0; c<tet1; c++)
{   glBegin(GL_LINE_LOOP);
        glVertex3f(ve[0][c].x, ve[0][c].y, ve[0][c].z);
        glVertex3f( e[0][c].x,  e[0][c].y,  e[0][c].z);
        glVertex3f(   qt[c].x,    qt[c].y,    qt[c].z);
        glVertex3f( e[2][c].x,  e[2][c].y,  e[2][c].z);   glEnd();
    glBegin(GL_LINE_LOOP);
          glVertex3f( e[0][c].x,  e[0][c].y,  e[0][c].z);
        glVertex3f(ve[1][c].x, ve[1][c].y, ve[1][c].z);
        glVertex3f( e[1][c].x,  e[1][c].y,  e[1][c].z);
        glVertex3f(   qt[c].x,    qt[c].y, qt[c].z);glEnd();
    glBegin(GL_LINE_LOOP);
        glVertex3f(   qt[c].x,    qt[c].y, qt[c].z);
        glVertex3f( e[1][c].x,  e[1][c].y,  e[1][c].z);
        glVertex3f(ve[2][c].x, ve[2][c].y, ve[2][c].z);
        glVertex3f( e[2][c].x,  e[2][c].y,  e[2][c].z);glEnd();
} 
montaVetorTetra1();
tetraedroIter2();

   for(int c=0; c<tet2; c++)
{  glBegin(GL_LINE_LOOP);
 glVertex3f(ve_2[0][c].x, ve_2[0][c].y, ve_2[0][c].z); 
 glVertex3f(e_2[0][c].x, e_2[0][c].y, e_2[0][c].z); 
 glVertex3f(qt_2[c].x, qt_2[c].y, qt_2[c].z);
 glVertex3f(e_2[3][c].x, e_2[3][c].y, e_2[3][c].z);glEnd();
 
 glBegin(GL_LINE_LOOP);
 glVertex3f(e_2[0][c].x, e_2[0][c].y, e_2[0][c].z);
 glVertex3f(ve_2[1][c].x, ve_2[1][c].y, ve_2[1][c].z);
 glVertex3f(e_2[1][c].x, e_2[1][c].y, e_2[1][c].z); 
 glVertex3f(qt_2[c].x, qt_2[c].y, qt_2[c].z);glEnd();
 
 glBegin(GL_LINE_LOOP);
 glVertex3f(qt_2[c].x, qt_2[c].y, qt_2[c].z);
 glVertex3f(e_2[1][c].x, e_2[1][c].y, e_2[1][c].z);
 glVertex3f(ve_2[2][c].x, ve_2[2][c].y, ve_2[2][c].z); 
 glVertex3f(e_2[2][c].x, e_2[2][c].y, e_2[2][c].z);glEnd();
 
 glBegin(GL_LINE_LOOP);
 glVertex3f(e_2[3][c].x, e_2[3][c].y, e_2[3][c].z);
 glVertex3f(qt_2[c].x, qt_2[c].y, qt_2[c].z);
 glVertex3f(e_2[2][c].x, e_2[2][c].y, e_2[2][c].z); 
 glVertex3f(ve_2[3][c].x, ve_2[3][c].y, ve_2[3][c].z);
 glEnd();
}
montaVetorTetra2();
tetraedroIter3();

for(int c=0; c<tet3; c++)//
{  glBegin(GL_LINE_LOOP);
 glVertex3f(ve_3[0][c].x, ve_3[0][c].y, ve_3[0][c].z); 
 glVertex3f(e_3[0][c].x, e_3[0][c].y, e_3[0][c].z); 
 glVertex3f(qt_3[c].x, qt_3[c].y, qt_3[c].z);
 glVertex3f(e_3[3][c].x, e_3[3][c].y, e_3[3][c].z);glEnd();
 
 glBegin(GL_LINE_LOOP);
 glVertex3f(e_3[0][c].x, e_3[0][c].y, e_3[0][c].z);
 glVertex3f(ve_3[1][c].x, ve_3[1][c].y, ve_3[1][c].z);
 glVertex3f(e_3[1][c].x, e_3[1][c].y, e_3[1][c].z); 
 glVertex3f(qt_3[c].x, qt_3[c].y, qt_3[c].z);glEnd();
 
 glBegin(GL_LINE_LOOP);
 glVertex3f(qt_3[c].x, qt_3[c].y, qt_3[c].z);
 glVertex3f(e_3[1][c].x, e_3[1][c].y, e_3[1][c].z);
 glVertex3f(ve_3[2][c].x, ve_3[2][c].y, ve_3[2][c].z); 
 glVertex3f(e_3[2][c].x, e_3[2][c].y, e_3[2][c].z);glEnd();
 
 glBegin(GL_LINE_LOOP);
 glVertex3f(e_3[3][c].x, e_3[3][c].y, e_3[3][c].z);
 glVertex3f(qt_3[c].x, qt_3[c].y, qt_3[c].z);
 glVertex3f(e_3[2][c].x, e_3[2][c].y, e_3[2][c].z); 
 glVertex3f(ve_3[3][c].x, ve_3[3][c].y, ve_3[3][c].z);
 glEnd();
}

 //Tratamos agora da suavização do HEXAEDRO

//para calc
    PontoXYZ p11; p11.x = he[0][0][0]; p11.y = he[0][0][1]; p11.z = he[0][0][2];
    PontoXYZ p12; p12.x = he[0][1][0]; p12.y = he[0][1][1]; p12.z = he[0][1][2];
    PontoXYZ p13; p13.x = he[0][2][0]; p13.y = he[0][2][1]; p13.z = he[0][2][2];
    PontoXYZ p14; p14.x = he[0][3][0]; p14.y = he[0][3][1]; p14.z = he[0][3][2];

    PontoXYZ p21 = p11;//=p11, p61
    PontoXYZ p22 = p14;//=p14, p31
    PontoXYZ p23; p23.x = he[1][2][0]; p23.y = he[1][2][1]; p23.z = he[1][2][2];
    PontoXYZ p24; p24.x = he[1][3][0]; p24.y = he[1][3][1]; p24.z = he[1][3][2];

    PontoXYZ p31 = p22;//=p14, p22
    PontoXYZ p32 = p13;//=p54, p13
    PontoXYZ p33; p33.x = he[2][2][0]; p33.y = he[2][2][1]; p33.z = he[2][2][2];
    PontoXYZ p34 = p23;//=p42, p23
    
    PontoXYZ p41 = p24;//=p62, p24
    PontoXYZ p42 = p23;//=p34, p23
    PontoXYZ p43 = p33;//=p53, p33
    PontoXYZ p44; p44.x = he[3][3][0]; p44.y = he[3][3][1]; p44.z = he[3][3][2];
    
    PontoXYZ p51 = p12;//=p64
    PontoXYZ p52 = p44;//=p63
    PontoXYZ p53 = p33;//=p43
    PontoXYZ p54 = p13;//=p32
    
    PontoXYZ p61 = p11;//=p21
    PontoXYZ p62 = p24;//=p41
    PontoXYZ p63 = p44;//=p52
    PontoXYZ p64 = p12;//=p51
    
    //pontos nas faces
    q1 = q[0][0] = (p11 + p12 + p13 + p14)/4;
    q2 = q[0][1] = (p21 + p22 + p23 + p24)/4;
    q3 = q[0][2] = (p31 + p32 + p33 + p34)/4;
    q4 = q[0][3] = (p41 + p42 + p43 + p44)/4;
    q5 = q[0][4] = (p51 + p52 + p53 + p54)/4;
    q6 = q[0][5] = (p61 + p62 + p63 + p64)/4;

    //pontos nas linhas de intersecção
PontoXYZ i12 = t[3][0] = (q1+q2)/4 + (p21+p22)/4;
PontoXYZ i13 = t[2][0] = (q1+q3)/4 + (p31+p32)/4;
PontoXYZ i15 = t[1][0] = (q1+q5)/4 + (p51+p54)/4;
PontoXYZ i16 = t[0][0] = (q1+q6)/4 + (p61+p64)/4;

PontoXYZ i21 = t[1][1] = i12;
PontoXYZ i23 = t[2][1] = (q2+q3)/4 + (p31+p34)/4;
PontoXYZ i24 = t[3][1] = (q2+q4)/4 + (p41+p42)/4;
PontoXYZ i26 = t[0][1] = (q2+q6)/4 + (p61+p62)/4;

PontoXYZ i31 = t[0][2] = i13;
PontoXYZ i32 = t[3][2] = i23;
PontoXYZ i34 = t[2][2] = (q3+q4)/4 + (p42+p43)/4;
PontoXYZ i35 = t[1][2] = (q3+q5)/4 + (p53+p54)/4;

PontoXYZ i42 = t[1][3] = i24;
PontoXYZ i43 = t[2][3] = i34;
PontoXYZ i45 = t[3][3] = (q4+q5)/4 + (p52+p53)/4;
PontoXYZ i46 = t[0][3] = (q4+q6)/4 + (p62+p63)/4;

PontoXYZ i51 = t[3][4] = i15;
PontoXYZ i53 = t[2][4] = i35;
PontoXYZ i54 = t[1][4] = i45;
PontoXYZ i56 = t[0][4] = (q5+q6)/4 + (p63+p64)/4;
    
PontoXYZ i61 = t[2][5] = i16;
PontoXYZ i62 = t[3][5] = i26;
PontoXYZ i64 = t[0][5] = i46;
PontoXYZ i65 = t[1][5] = i56;
    
    //pontos de vértice = Q/4+2R/n+S(n-3)/n
    PontoXYZ v11 = v[0][0] = p11/4 + (q1+q2+q6)/12 + ((p11+p12)/2+(p11+p14)/2+(p11+p62)/2)/6;
    PontoXYZ v12 = v[1][0] = p12/4 + (q1+q5+q6)/12 + ((p12+p13)/2+(p12+p11)/2+(p12+p52)/2)/6;
    PontoXYZ v13 = v[2][0] = p13/4 + (q1+q3+q5)/12 + ((p13+p14)/2+(p13+p12)/2+(p13+p33)/2)/6;
    PontoXYZ v14 = v[3][0] = p14/4 + (q1+q2+q3)/12 + ((p14+p11)/2+(p14+p13)/2+(p14+p23)/2)/6;

    PontoXYZ v21 = v[1][1] = v11;
    PontoXYZ v22 = v[2][1] = v14;
    PontoXYZ v23 = v[3][1] = p23/4 + (q2+q3+q4)/12 + ((p23+p22)/2+(p23+p24)/2+(p23+p43)/2)/6;
    PontoXYZ v24 = v[0][1] = p24/4 + (q2+q4+q6)/12 + ((p24+p23)/2+(p24+p21)/2+(p24+p44)/2)/6;

    PontoXYZ v31 = v[0][2] = v14;
    PontoXYZ v32 = v[1][2] = v13;
    PontoXYZ v33 = v[2][2] = p33/4 + (q3+q5+q4)/12 + ((p33+p32)/2+(p33+p34)/2+(p33+p52)/2)/6;
    PontoXYZ v34 = v[3][2] = v23;

    PontoXYZ v41 = v[1][3] = v24;
    PontoXYZ v42 = v[2][3] = v23;
    PontoXYZ v43 = v[3][3] = v33;
    PontoXYZ v44 = v[0][3] = p44/4 + (q4+q5+q6)/12 + ((p44+p41)/2+(p44+p43)/2+(p44+p51)/2)/6;

    PontoXYZ v51 = v[0][4] = v12;
    PontoXYZ v52 = v[1][4] = v44;
    PontoXYZ v53 = v[2][4] = v33;
    PontoXYZ v54 = v[3][4] = v13;

    PontoXYZ v61 = v[3][5] = v11;
    PontoXYZ v62 = v[0][5] = v24;
    PontoXYZ v63 = v[1][5] = v44;
    PontoXYZ v64 = v[2][5] = v12;
    

//desenhando o resultado da 1a iteração
for (i = 0; i < hex1; i++)
{
    glBegin(GL_LINE_LOOP);
        glVertex3f(v[0][i].x, v[0][i].y, v[0][i].z);
        glVertex3f(t[0][i].x, t[0][i].y, t[0][i].z);
        glVertex3f(q[0][i].x, q[0][i].y, q[0][i].z);
        glVertex3f(t[3][i].x, t[3][i].y, t[3][i].z);
    glEnd();
    glBegin(GL_LINE_LOOP);
        glVertex3f(t[0][i].x, t[0][i].y, t[0][i].z);
        glVertex3f(v[1][i].x, v[1][i].y, v[1][i].z);
        glVertex3f(t[1][i].x, t[1][i].y, t[1][i].z);
        glVertex3f(q[0][i].x, q[0][i].y, q[0][i].z);
    glEnd();
    glBegin(GL_LINE_LOOP);
        glVertex3f(q[0][i].x, q[0][i].y, q[0][i].z);
        glVertex3f(t[1][i].x, t[1][i].y, t[1][i].z);
        glVertex3f(v[2][i].x, v[2][i].y, v[2][i].z);
        glVertex3f(t[2][i].x, t[2][i].y, t[2][i].z);
    glEnd();
    glBegin(GL_LINE_LOOP);
        glVertex3f(t[3][i].x, t[3][i].y, t[3][i].z);
        glVertex3f(q[0][i].x, q[0][i].y, q[0][i].z);
        glVertex3f(t[2][i].x, t[2][i].y, t[2][i].z);
        glVertex3f(v[3][i].x, v[3][i].y, v[3][i].z);
    glEnd();
}

montaVetor1();
iteracao2();
//desenhando o resultado da 2a iteração
for(i=0; i<hex2; i++)
{
    glBegin(GL_LINE_LOOP);
        glVertex3f(v_2[0][i].x, v_2[0][i].y, v_2[0][i].z);
        glVertex3f(t_2[0][i].x, t_2[0][i].y, t_2[0][i].z);
        glVertex3f(q_2[i].x, q_2[i].y, q_2[i].z);
        glVertex3f(t_2[3][i].x, t_2[3][i].y, t_2[3][i].z);
    glEnd();
    glBegin(GL_LINE_LOOP);
        glVertex3f(t_2[0][i].x, t_2[0][i].y, t_2[0][i].z);
        glVertex3f(v_2[1][i].x, v_2[1][i].y, v_2[1][i].z);
        glVertex3f(t_2[1][i].x, t_2[1][i].y, t_2[1][i].z);
        glVertex3f(q_2[i].x, q_2[i].y, q_2[i].z);
    glEnd();
    glBegin(GL_LINE_LOOP);
        glVertex3f(q_2[i].x, q_2[i].y, q_2[i].z);
        glVertex3f(t_2[1][i].x, t_2[1][i].y, t_2[1][i].z);
        glVertex3f(v_2[2][i].x, v_2[2][i].y, v_2[2][i].z);
        glVertex3f(t_2[2][i].x, t_2[2][i].y, t_2[2][i].z);
    glEnd();
    glBegin(GL_LINE_LOOP);
        glVertex3f(t_2[3][i].x, t_2[3][i].y, t_2[3][i].z);
        glVertex3f(q_2[i].x, q_2[i].y, q_2[i].z);
        glVertex3f(t_2[2][i].x, t_2[2][i].y, t_2[2][i].z);
        glVertex3f(v_2[3][i].x, v_2[3][i].y, v_2[3][i].z);
    glEnd();
}

montaVetor2();
iteracao3();

//desenhando o resultado da 3a iteração
for(i=0; i<hex3; i++)
{
    glBegin(GL_LINE_LOOP);
        glVertex3f(v_3[0][i].x, v_3[0][i].y, v_3[0][i].z);
        glVertex3f(t_3[0][i].x, t_3[0][i].y, t_3[0][i].z);
        glVertex3f(q_3[i].x,       q_3[i].y, q_3[i].z);
        glVertex3f(t_3[3][i].x, t_3[3][i].y, t_3[3][i].z);
    glEnd(); 
    glBegin(GL_LINE_LOOP);
        glVertex3f(t_3[0][i].x, t_3[0][i].y, t_3[0][i].z);
        glVertex3f(v_3[1][i].x, v_3[1][i].y, v_3[1][i].z);
        glVertex3f(t_3[1][i].x, t_3[1][i].y, t_3[1][i].z);
        glVertex3f(q_3[i].x, q_3[i].y, q_3[i].z);
    glEnd(); 
    glBegin(GL_LINE_LOOP);
        glVertex3f(q_3[i].x, q_3[i].y, q_3[i].z);
        glVertex3f(t_3[1][i].x, t_3[1][i].y, t_3[1][i].z);
        glVertex3f(v_3[2][i].x, v_3[2][i].y, v_3[2][i].z);
        glVertex3f(t_3[2][i].x, t_3[2][i].y, t_3[2][i].z);
    glEnd();
    glBegin(GL_LINE_LOOP);
        glVertex3f(t_3[3][i].x, t_3[3][i].y, t_3[3][i].z);
        glVertex3f(q_3[i].x, q_3[i].y, q_3[i].z);
        glVertex3f(t_3[2][i].x, t_3[2][i].y, t_3[2][i].z);
        glVertex3f(v_3[3][i].x, v_3[3][i].y, v_3[3][i].z);
    glEnd(); 
}

//desenhando o hexágono
for(i=0;i<hex;i++)
{
    if (isLine) glBegin(GL_LINE_LOOP);
    else glBegin(GL_POLYGON);

        glColor3f (1/he[i][0][0], 1/he[i][0][1], 1/he[i][0][2]);
        glVertex3f(he[i][0][0],he[i][0][1],he[i][0][2]);
        glColor3f (1/he[i][1][0], 1/he[i][1][1], 1/he[i][1][2]);
        glVertex3f(he[i][1][0],he[i][1][1],he[i][1][2]);
        glColor3f (1/he[i][2][0], 1/he[i][2][1], 1/he[i][2][2]);
        glVertex3f(he[i][2][0],he[i][2][1],he[i][2][2]);
        glColor3f (1/he[i][3][0], 1/he[i][3][1], 1/he[i][3][2]);
        glVertex3f(he[i][3][0],he[i][3][1],he[i][3][2]);
    glEnd();
}



	// Flush dos comandos de desenho que estejam no "pipeline" da OpenGL
    // para conclusao da geracao da imagem
    glFlush();
       
}


// Inicializa aspectos do rendering
void SetupRC(void)
{
    glClearColor(0.1f, 0.1f, 0.1f, 1.0f);  // cor de fundo da janela
}

// Especifica callback comum de teclado     
void KeyboardFunc ( unsigned char key, int x, int y )
{
    switch (key)                 
    {                 
         case 'x' : glRotatef(-5,1,0,0); break;
         case 'X' : glRotatef(5,1,0,0);  break;
         case 'y' : glRotatef(-5,0,1,0); break;
         case 'Y' : glRotatef(5,0,1,0);  break;
         case 'z' : glRotatef(-5,0,0,1); break;
         case 'Z' : glRotatef(5,0,0,1);  break;
    
         case 'f' : isFlat = 1; break;
         case 'F' : isFlat = 0; break;
         case 'l' : isLine = 1; break;
         case 'L' : isLine = 0; break;
         
         case '1' : whatIs = 1; break;
         case '2' : whatIs = 2; break;
         case '3' : whatIs = 3; break;
         case '4' : whatIs = 4; break;
         case '5' : whatIs = 5; break;
         case '6' : whatIs = 6; break;
         case '7' : whatIs = 7; break;
         case '8' : whatIs = 8; break;
         
         case 27  : exit(0); break;
         default  : break;
     }
     glutPostRedisplay();     
}


// Cria janela 
// Inicializa aspectos relacionados a janela e a geracao da imagem
// Especifica a função de callback de desenho
// Especifica funções de callback de teclado para teclas normais e especiais
int main(void)
    {
	// Indica que deve ser usado um unico buffer para armazenamento da imagem e representacao de cores RGB
    glutInitDisplayMode(GLUT_SINGLE | GLUT_RGB);
    glutInitWindowPosition(60,60);
    glutInitWindowSize(500,500);   

    // Cria uma janela com o titulo especificado
	glutCreateWindow("Sólidos Platônicos Suavizados");

    // Especifica a funcao que vai tratar teclas comuns 
    glutKeyboardFunc(KeyboardFunc);
  
    // Especifica para a OpenGL que funcao deve ser chamada para geracao da imagem
	glutDisplayFunc(RenderScene);

    // Executa a inicializacao de parametros de exibicao
	SetupRC();

    // Dispara a "maquina de estados" de OpenGL 
	glutMainLoop();
	return 0;
    }