asympt04

\begin{asy}
size(200);
import palette;
import three;

currentprojection=orthographic(1,1,1);

triple[] M={
  (-1,-1,-1),(0,-1,-1),(1,-1,-1),(1,0,-1),
  (1,1,-1),(0,1,-1),(-1,1,-1),(-1,0,-1),
  (-1,-1,0),(1,-1,0),(1,1,0),(-1,1,0),
  (-1,-1,1),(0,-1,1),(1,-1,1),(1,0,1),(1,1,1),(0,1,1),(-1,1,1),(-1,0,1)
};

surface[] Squares={
  surface((1,-1,-1)--(1,1,-1)--(1,1,1)--(1,-1,1)--cycle),
  surface((-1,-1,-1)--(-1,1,-1)--(-1,1,1)--(-1,-1,1)--cycle),
  surface((1,1,-1)--(-1,1,-1)--(-1,1,1)--(1,1,1)--cycle),
  surface((1,-1,-1)--(-1,-1,-1)--(-1,-1,1)--(1,-1,1)--cycle),
  surface((1,-1,1)--(1,1,1)--(-1,1,1)--(-1,-1,1)--cycle),
  surface((1,-1,-1)--(1,1,-1)--(-1,1,-1)--(-1,-1,-1)--cycle),
};

int[][] SquaresPoints={
  {2,3,4,10,16,15,14,9},
  {0,7,6,11,18,19,12,8},
  {4,5,6,11,18,17,16,10},
  {2,1,0,8,12,13,14,9},
  {12,13,14,15,16,17,18,19},
  {0,1,2,3,4,5,6,7}
};

int[][] index={
  {0,2,4},{0,1},{1,2,4},{2,3},{1,3,4},{0,1},{0,3,4},{2,3},
  {4,5},{4,5},{4,5},{4,5},
  {0,2,5},{0,1},{1,2,5},{2,3},{1,3,5},{0,1},{0,3,5},{2,3}
};

int[] Sponge0=array(n=6,value=1);

int[] eraseFaces(int n, int[] Sponge0) {
  int[] temp=copy(Sponge0);
  for(int k : index[n]) {
    temp[k]=0;
  }
  return temp;
}

int[][] Sponge1=new int[20][];
for(int n=0; n < 20; ++n) {
  Sponge1[n]=eraseFaces(n,Sponge0);
}

int[][] eraseFaces(int n, int[][] Sponge1) {
  int[][] temp=copy(Sponge1);
  for(int k : index[n])
    for(int n1 : SquaresPoints[k])
      temp[n1][k]=0;
  return temp;
}

int[][][] Sponge2=new int[20][][];
for(int n=0; n < 20; ++n)
  Sponge2[n]=eraseFaces(n,Sponge1);

int[][][] eraseFaces(int n, int[][][] Sponge2) {
  int[][][] temp=copy(Sponge2);
  for(int k : index[n])
    for(int n2: SquaresPoints[k])
      for(int n1: SquaresPoints[k])
        temp[n2][n1][k]=0;
  return temp;
}

int[][][][] Sponge3=new int[20][][][];
for(int n=0; n < 20; ++n)
  Sponge3[n]=eraseFaces(n,Sponge2);

surface s3;
real u=2/3;
for(int n3=0; n3 < 20; ++n3) {
  surface s2;
  for(int n2=0; n2 < 20; ++n2) {
    surface s1;
    for(int n1=0; n1 < 20; ++n1) {
      for(int k=0; k < 6; ++k){
        transform3 T=scale3(u)*shift(M[n1])*scale3(0.5);
        if(Sponge3[n3][n2][n1][k] > 0) {
          s1.append(T*Squares[k]);
        }
      }
    }
    transform3 T=scale3(u)*shift(M[n2])*scale3(0.5);
    s2.append(T*s1);
  }
  transform3 T=scale3(u)*shift(M[n3])*scale3(0.5);
  s3.append(T*s2);
}
s3.colors(palette(s3.map(abs),Rainbow()));
draw(s3);

\end{asy}