JSCAD script console.logs Mathematica command FindHamiltonianCycle[...], and displays its results in JSCAD

C60.Hamilton_Cycle.jscad

"use strict"
const jscad = require('@jscad/modeling')
const { translate, rotate, scale:scale3d } = jscad.transforms
const { vec3 } = jscad.maths
const { colorize } = jscad.colors
const { sphere, cylinder } = jscad.primitives
const { add, length, subtract, scale } = jscad.maths.vec3

const phi=(Math.sqrt(5)+1)/2;
const build=[[0,1,3*phi],[1,2+phi,2*phi],[phi,2,2*phi+1]];

const coords =[];

build.forEach((v) => {
  for(var o=0;o<3;++o){
    var w=[];
    for(var i=0;i<3;++i)
      w.push(v[(o+i)%3]);
    
    for(var a=-1;a<=(w[0]!=0);a+=2)
      for(var b=-1;b<=(w[1]!=0);b+=2)
        for(var c=-1;c<=(w[2]!=0);c+=2)
          coords.push([a*w[0],b*w[1],c*w[2]]);
  }
})

var edges=[];
var e=-1;
var E=[];
for(var v=0;v<coords.length;++v) {
  edges.push([]);
}
for(var v=0;v<coords.length;++v) {
  for(var w=v+1;w<coords.length;++w) {
    // check for golden ratio vertex coordinates edge length
    if(vec3.distance(coords[v],coords[w])==2) { 
      e+=1;
      E.push([v,w]);
      edges[v].push(e);
      edges[w].push(e);
    }
  }
}

function vertex(_v) {
    return(translate(_v, sphere({radius: 0.1})));
}

function edge2(_v, _w, r = 0.05) {
    var d = [0, 0, 0];
    var w = [0, 0, 0];
    subtract(d, _w, _v);
    add(w, _v, _w);
    scale(w, w, 0.5);
    return translate(w,
             rotate([0, Math.acos(d[2]/length(d)), Math.atan2(d[1], d[0])],
               scale3d([r,r,length(d)],cylinder({radius: 1, height: 1}))
             )
           );
}

function edge(_e, r = 0.05) {
    return edge2(coords[_e[0]],coords[_e[1]]);
}

function main() {
  var out = [];
  coords.forEach((v) => out.push(colorize([0,0.5,1],vertex(v))));

  var cmd = "FindHamiltonianCycle[Graph[{";
  E.forEach((e,i) => {
//    out.push(colorize([0,0.5,1,0.1],edge(e)));
    cmd+=(i==0?"":",")+"UndirectedEdge["+e[0]+","+e[1]+"]";
  });
  cmd+="}]]";
  console.log(cmd);
  
  var hc=[0,36,28,52,8,9,55,31,39,3,43,35,59,27,26,50,18,14,46,5,7,51,
          19,15,47,23,22,54,30,38,2,42,34,58,10,11,57,33,41,1,37,29,
          53,21,20,44,12,16,48,6,4,45,13,17,49,25,24,56,32,40];
  var old=hc[hc.length-1];
  hc.forEach((v) => {out.push(colorize([1,0,0],edge([old,v])));old=v;});
  
  return out;
}

module.exports = { main }

Detailed description here:
https://forums.raspberrypi.com/viewtopic.php?p=2317762#p2317762

Motivated by

which is Hamiltonian Cycle of C60 (football) fullerene

now looks like below:
https://jscad.app/#https://gist.githubusercontent.com/Hermann-SW/981fc580814f8bda5689b7eb1b4bd751/raw/38d0c8b477e5a238065137c9c7f68fa6df0d4837/C60.Hamilton_Cycle.jscad