import graph3; size(400); currentlight.background=palegreen; defaultrender=render(compression=Zero,merge=true); real c=(1+sqrt(5))/2; triple[] z={(c,1,0),(-c,1,0),(-c,-1,0),(c,-1,0)}; triple[] x={(0,c,1),(0,-c,1),(0,-c,-1),(0,c,-1)}; triple[] y={(1,0,c),(1,0,-c),(-1,0,-c),(-1,0,c)}; triple[][] Q={ {z[0],y[1],x[3],x[0],y[0],z[3]}, {z[1],x[0],x[3],y[2],z[2],y[3]}, {z[2],z[1],y[2],x[2],x[1],y[3]}, {z[3],z[0],y[0],x[1],x[2],y[1]}, {x[0],x[3],z[1],y[3],y[0],z[0]}, {x[1],x[2],z[2],y[3],y[0],z[3]}, {x[2],x[1],z[3],y[1],y[2],z[2]}, {x[3],x[0],z[0],y[1],y[2],z[1]}, {y[0],y[3],x[1],z[3],z[0],x[0]}, {y[1],y[2],x[2],z[3],z[0],x[3]}, {y[2],y[1],x[3],z[1],z[2],x[2]}, {y[3],y[0],x[0],z[1],z[2],x[1]} }; path3 p=arc(O,Q[0][0],Q[0][1]); real R=abs(point(p,reltime(p,1/3))); triple[][] P; for(int i=0; i < Q.length; ++i){ P[i]=new triple[] ; for(int j=0; j < Q[i].length; ++j){ P[i][j]=Q[i][j]/R; } } surface sphericaltriangle(triple center, triple A, triple B, triple C, int nu=3, int nv=nu) { path3 tri1=arc(center,A,B); path3 tri2=arc(center,A,C); path3 tri3=arc(center,B,C); triple tri(pair p) { path3 cr=arc(O,relpoint(tri2,p.x),relpoint(tri3,p.x)); return relpoint(cr,p.y); }; return surface(tri,(0,0),(1-sqrtEpsilon,1),nu,nv,Spline); } for(int i=0; i < P.length; ++i){ triple[] pentagon=sequence(new triple(int k) { path3 p=arc(O,P[i][0],P[i][k+1]); return point(p,reltime(p,1/3)); },5); pentagon.cyclic=true; draw(sequence(new path3(int k) { return arc(O,pentagon[k],pentagon[k+1]);},5),linewidth(2pt)); triple M=unit(sum(pentagon)/5); for(int i=0; i < 5; ++i){ surface sf=sphericaltriangle(O,pentagon[i],M,pentagon[i+1]); draw(sf,black); } } for(int i=0; i < P.length; ++i){ for(int j=1; j <= 5; ++j){ triple K=P[i][0]; triple A=P[i][j]; triple B=P[i][(j % 5)+1]; path3[] p={arc(O,K,A),arc(O,A,B),arc(O,B,K)}; draw(subpath(p[0],reltime(p[0],1/3),reltime(p[0],2/3)),linewidth(4pt)); triple[] hexagon={point(p[0],reltime(p[0],1/3)), point(p[0],reltime(p[0],2/3)), point(p[1],reltime(p[1],1/3)), point(p[1],reltime(p[1],2/3)), point(p[2],reltime(p[2],1/3)), point(p[2],reltime(p[2],2/3))}; hexagon.cyclic=true; triple M=unit(sum(hexagon)/6); for(int i=0; i < 6; ++i){ surface sf=sphericaltriangle(O,hexagon[i],M,hexagon[i+1]); draw(sf,white); } } }