File:120-cell petrie polygon.svg
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Summary
Description120-cell petrie polygon.svg |
English: Special orthographic projection of 120-cell making the petrie polygon |
Date | |
Source | Own work |
Author | Claudio Rocchini |
/*********************************
* Drawing the 120-cell Petrie Polygon
* (C) 2008 Claudio Rocchini
* CC-BY 3.0
*********************************/
bool even_permutation( int p[], int n )
{
int i,ns;
int * pt = new int[n];
for(i=0;i<n;++i) pt[i] = p[i];
ns = 0;
for(;;) {
int j,k;
for(j=0;j<n;++j) if(pt[j]!=j) break;
if(j==n) break;
for(k=0;k<n;++k) if(pt[k]==j) break;
std::swap(pt[k],pt[j]);
++ns;
}
delete[] pt;
return ns%2==0;
}
void main()
{
const double EPS = 1e-6;
const int ND = 4;
const int NV = 600; const int NE = 1200;
const double fi = (1+sqrt(5))/2; const double fi2 = fi*fi;
const double rfi = pow(fi,-1); const double rfi2 = pow(fi,-2);
double v[NV][ND]; int e[NE][2];
double px[NV]; double py[NV];
// Magic numbers: hard to find projection directions
const double PX[ND] = {-0.11317046518674401,-0.13682953481325594,-0.09854835601535949,-0.29133803200072961};
const double PY[ND] = { 0.19601699561964564, 0.23699570627257371,-0.05689691987366302,-0.16820409120079699};
int i,j,k,l;
int i1,i2,i3,i4;
k = 0;
for(i1= 0;i1<4-1;++i1) for(i2=i1+1;i2<4 ;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
v[k][ 0] = v[k][ 1] = v[k][ 2] = v[k][ 3] = 0;
v[k][i1] = -2+4*i3;
v[k][i2] = -2+4*i4;
++k;
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
v[k][0] = -1+2*i1; v[k][1] = -1+2*i2; v[k][2] = -1+2*i3; v[k][3] = i4==0 ? -sqrt(5) : sqrt(5); ++k;
v[k][0] = -1+2*i1; v[k][1] = -1+2*i2; v[k][2] = i3==0 ? -sqrt(5) : sqrt(5); v[k][3] = -1+2*i4; ++k;
v[k][0] = -1+2*i1; v[k][1] = i2==0 ? -sqrt(5) : sqrt(5); v[k][2] = -1+2*i3; v[k][3] = -1+2*i4; ++k;
v[k][0] = i1==0 ? -sqrt(5) : sqrt(5); v[k][1] = -1+2*i2; v[k][2] = -1+2*i3; v[k][3] = -1+2*i4; ++k;;
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
v[k][0] = i1==0?-fi:fi; v[k][1] = i2==0?-fi:fi; v[k][2] = i3==0?-fi:fi; v[k][3] = i4==0?-rfi2:rfi2; ++k;
v[k][0] = i1==0?-fi:fi; v[k][1] = i2==0?-fi:fi; v[k][2] = i3==0?-rfi2:rfi2; v[k][3] = i4==0?-fi:fi; ++k;
v[k][0] = i1==0?-fi:fi; v[k][1] = i2==0?-rfi2:rfi2; v[k][2] = i3==0?-fi:fi; v[k][3] = i4==0?-fi:fi; ++k;
v[k][0] = i1==0?-rfi2:rfi2; v[k][1] = i2==0?-fi:fi; v[k][2] = i3==0?-fi:fi; v[k][3] = i4==0?-fi:fi; ++k;
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
v[k][0] = i1==0?-rfi:rfi; v[k][1] = i2==0?-rfi:rfi; v[k][2] = i3==0?-rfi:rfi; v[k][3] = i4==0?-fi2:fi2; ++k;
v[k][0] = i1==0?-rfi:rfi; v[k][1] = i2==0?-rfi:rfi; v[k][2] = i3==0?-fi2:fi2; v[k][3] = i4==0?-rfi:rfi; ++k;
v[k][0] = i1==0?-rfi:rfi; v[k][1] = i2==0?-fi2:fi2; v[k][2] = i3==0?-rfi:rfi; v[k][3] = i4==0?-rfi:rfi; ++k;
v[k][0] = i1==0?-fi2:fi2; v[k][1] = i2==0?-rfi:rfi; v[k][2] = i3==0?-rfi:rfi; v[k][3] = i4==0?-rfi:rfi; ++k;
}
double val[4]; int per[4];
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2) for(i3=0;i3<2;++i3) {
val[0] = 0;
val[1] = i1==0 ? -rfi2 : rfi2;
val[2] = i2==0 ? -1 : 1;
val[3] = i3==0 ? -fi2 : fi2;
for(i=0;i<4;++i) per[i] = i;
do {
if(even_permutation(per,4)) { for(i=0;i<4;++i) v[k][i] = val[per[i]]; ++k; }
} while(std::next_permutation(per,per+4));
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2) for(i3=0;i3<2;++i3) {
val[0] = 0;
val[1] = i1==0 ? -rfi : rfi;
val[2] = i2==0 ? -fi : fi;
val[3] = i3==0 ? -sqrt(5) : sqrt(5);
for(i=0;i<4;++i) per[i] = i;
do {
if(even_permutation(per,4)) { for(i=0;i<4;++i) v[k][i] = val[per[i]]; ++k; }
} while(std::next_permutation(per,per+4));
}
for(i1=0;i1<2;++i1) for(i2=0;i2<2;++i2)
for(i3=0;i3<2;++i3) for(i4=0;i4<2;++i4) {
val[0] = i1==0 ? -rfi : rfi;
val[1] = i2==0 ? -1 : 1;
val[2] = i3==0 ? -fi : fi;
val[3] = i4==0 ? -2 : 2;
for(i=0;i<4;++i) per[i] = i;
do {
if(even_permutation(per,4)) { for(i=0;i<4;++i) v[k][i] = val[per[i]]; ++k; }
} while(std::next_permutation(per,per+4));
}
assert(k==NV);
const double de = 0.76393202250021019;
k = 0;
for(i= 0;i<NV-1;++i)
for(j=i+1;j<NV ;++j) {
double d = 0;
for(l=0;l<ND;++l) d += (v[i][l]-v[j][l])*(v[i][l]-v[j][l]);
d = sqrt(d);
if( fabs(de-d)<EPS ) { e[k][0] = i; e[k][1] = j; ++k; }
}
assert(k==NE);
for(i=0;i<NV;++i){
px[i] = 0; for(l=0;l<ND;++l) px[i] += v[i][l]*PX[l];
py[i] = 0; for(l=0;l<ND;++l) py[i] += v[i][l]*PY[l];
}
const double SX = 800; const double SY = 800;
const double B = 32; const double R = 6;
const double sca = std::min((SX-2*B)/2,(SY-2*B)/2);
for(i=0;i<NV;++i) { px[i] = B+(px[i]+1)*sca; py[i] = B+(py[i]+1)*sca; }
FILE * fp = fopen("c:\\temp\\New120Cell.svg","w");
fprintf(fp,
"<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n"
"<svg\n"
"xmlns:svg=\"http://www.w3.org/2000/svg\"\n"
"xmlns=\"http://www.w3.org/2000/svg\"\n"
"version=\"1.0\"\n"
"width=\"%g\"\n" "height=\"%g\"\n"
"id=\"New120Cell\">\n"
,SX,SY
);
fprintf(fp,"<g style=\"stroke:#000000;stroke-width:2;stroke-opacity:0.6;\">\n");
for(i=0;i<NE;++i)
fprintf(fp,
"<line x1=\"%5.1lf\" y1=\"%5.1lf\" x2=\"%5.1lf\" y2=\"%5.1lf\"/>\n"
,px[e[i][0]],py[e[i][0]], px[e[i][1]],py[e[i][1]]
);
fprintf(fp,"</g>\n");
fprintf(fp,"<g style=\"stroke:#000000;stroke-width:2;stroke-opacity:0.6;fill:#0080FF\">\n");
for(i=0;i<NV;++i)
fprintf(fp,"<circle cx=\"%5.1lf\" cy=\"%5.1lf\" r=\"%5.1lf\"/>\n",px[i],py[i],R);
fprintf(fp,"</g>\n");
fprintf(fp,"</svg>\n");
fclose(fp);
}
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Date/Time | Thumbnail | Dimensions | User | Comment | |
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current | 10:00, 1 August 2008 | ![]() | 800 × 800 (88 KB) | Rocchini | {{Information |Description={{en|1=Special orthographic projection of 120-cell making the petrie polygon}} |Source=Opera creata dall'uploader (own work by uploader) |Author=Claudio Rocchini |Date=2008-08-01 |Permission= |other_versions= } |
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