File:600-cell petrie polygon.svg
From Wikimedia Commons, the free media repository
Jump to navigation
Jump to search
Size of this PNG preview of this SVG file: 600 × 600 pixels. Other resolutions: 240 × 240 pixels | 480 × 480 pixels | 768 × 768 pixels | 1,024 × 1,024 pixels | 2,048 × 2,048 pixels.
Original file (SVG file, nominally 800 × 800 pixels, file size: 43 KB)
File information
Structured data
Captions
Summary
[edit]Description600-cell petrie polygon.svg |
English: Special orthographic projection of 600 Cell, making the petrie polygon |
Date | |
Source | Own work |
Author | Claudio Rocchini |
// Making the 600-cell petrie polygon
// (C)2008 Claudio Rocchini
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 = 120; const int NE = 720;
double v[NV][ND]; int e[NE][2];
double px[NV]; double py[NV];
// Magics! Hard to find projection directions
double PX[ND] = { 0.33086939364114176, 0.66913060635885813, 0.66913060635885824, 0.33086939364114182 };
double PY[ND] = { -0.74314482547739424, 0.07032846067420610, -0.07032846067420611, 0.74314482547739424 };
const double fi = (1.0+sqrt(5.0))/2.0;
const double le = 1.0/fi;
int i,j,k,l;
k = 0;
for(i=0;i<16;++i) {
for(j=0;j<ND;++j)
v[k][j] = -0.5 + ( i&(1<<j) ? 0 : 1 );
++k;
}
for(i=0;i<4;++i) for(j=0;j<2;++j) {
v[k][0] = v[k][1] = v[k][2] = v[k][3] = 0;
v[k][i] = -1+2*j;
++k;
}
for(j=0;j<8;++j) {
double val[4];
int per[4];
val[0] = 0;
val[1] = j&(1<<0) ? -0.5 : 0.5;
val[2] = j&(1<<1) ? -fi/2 : fi/2;
val[3] = j&(1<<2) ? -le/2 : le/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);
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(le-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\\New600Cell.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=\"New600Cell\">\n"
,SX,SY
);
fprintf(fp,"<g style=\"stroke:#000000;stroke-width:2;stroke-opacity:0.5;\">\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:0.5;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);
}
Licensing
[edit]I, the copyright holder of this work, hereby publish it under the following licenses:
Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue |
This file is licensed under the Creative Commons Attribution 3.0 Unported license.
- You are free:
- to share – to copy, distribute and transmit the work
- to remix – to adapt the work
- Under the following conditions:
- attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
You may select the license of your choice.
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 09:30, 1 August 2008 | 800 × 800 (43 KB) | Rocchini (talk | contribs) | {{Information |Description={{en|1=Special orthographic projection of 600 Cell, making the petrie polygon}} |Source=Opera creata dall'uploader (own work by uploader) |Author=Claudio Rocchini |Date=2008-08-01 |Permission= |other_versions= |
You cannot overwrite this file.
File usage on Commons
There are no pages that use this file.
File usage on other wikis
The following other wikis use this file:
- Usage on en.wikipedia.org
- Usage on fr.wikipedia.org
- Usage on simple.wikipedia.org
- Usage on sl.wikipedia.org