Got the vertices of the 120-cell looking ok

main.js

@@ -157,6 +157,7 @@ const STRUCTURES = {
 	'16-cell': POLYTOPES.cell16(),
 	'tesseract': POLYTOPES.tesseract(),
 	'24-cell': POLYTOPES.cell24(),
+	'120-cell': POLYTOPES.cell120()
 };
 
 console.log(STRUCTURES);
@@ -167,7 +168,7 @@ function createShape(name) {
 	if( shape ) {
 		scene.remove(shape);
 	}
-
+	console.log(STRUCTURES[name]);
 	shape = new FourDShape(node_ms, link_ms, STRUCTURES[name]);
 	scene.add(shape);
 
@@ -219,7 +220,7 @@ const gui_params = {
 };
 
 gui.add(gui_params, 'shape',
-	[ '5-cell', '16-cell', 'tesseract', '24-cell' ]
+	[ '5-cell', '16-cell', 'tesseract', '24-cell', '120-cell' ]
 	).onChange(createShape)
 
 gui.add(gui_params, 'hyperplane', 1.5, 4);

permute.js

@@ -28,15 +28,32 @@ function pandita(a) {
 	return false;
 }
 
+function permutations_old(a) {
+	a.sort();
+	const ps = [ [...a] ];
+	let running = true;
+	while( running ) {
+		const s = pandita(a);
+		if( s ) {
+			ps.push([...a]);
+		} else {
+			running = false;
+		}
+	}
+	return ps;
+}
+
 function permutations(a) {
 	a.sort();
 	const ps = [ [...a] ];
-	while( pandita(a) ) {
+	let running = true;
+	while( pandita(a) > 0 ) {
 		ps.push([...a]);
 	}
 	return ps;
 }
 
+
 function permutations_even(a) {
 	a.sort();
 	let parity = 'even';
@@ -64,4 +81,35 @@ function permutations_even(a) {
 	return ps;
 }
 
+// for a given permutation, say [ 1, 1, 0, 0 ], return all
+// of the valid changes of sign, so:
+// [ [1, 1, 0, 0 ], [ -1, 1, 0, 0 ], [ 1, -1, 0, 0 ], [-1, -1, 0, 0 ]]
+// ie don't do it on the zeros
+
+function expand_sign(a) {
+	const expanded = [];
+	const exv = a.map((v) => v ? [ -v, v ] : [ 0 ]);
+	for( const xv of exv[0] ) {
+		for( const yv of exv[1] ) {
+			for( const zv of exv[2] ) {
+				for( const wv of exv[3] ) {
+					expanded.push({x: xv, y:yv, z:zv, w:wv});
+				}
+			}
+		}
+	}
+	return expanded;
+}
+
+
+export function coordinates(a, even=false) {
+	const ps = even ? permutations_even(a) : permutations(a);
+	const coords = [];
+	for( const p of ps ) {
+		const expanded = expand_sign(p);
+		coords.push(...expanded);
+	}
+	return coords;
+}
+
 

polytopes.js

@@ -1,4 +1,5 @@
 
+import * as PERMUTE from './permute.js';
 
 export const cell5 = () => {
 	const r5 = Math.sqrt(5);
@@ -229,3 +230,40 @@ export const cell24 = () => {
 	};
 }
 
+
+function make_120cell_vertices() {
+	const phi = 0.5 * (1 + Math.sqrt(5));  3
+	const r5 = Math.sqrt(5);   5
+	const phi2 = phi * phi;    4
+	const phiinv = 1 / phi;    6
+	const phi2inv = 1 / phi2;  7
+
+	const nodes = [
+		PERMUTE.coordinates([2, 2, 0, 0]),
+		PERMUTE.coordinates([r5, 1, 1, 1]),
+		PERMUTE.coordinates([phi, phi, phi, phi2inv]),
+		PERMUTE.coordinates([phi, phiinv, phiinv, phiinv]),
+
+		PERMUTE.coordinates([phi2, phi2inv, 1, 0], true),
+		PERMUTE.coordinates([r5, phiinv, phi, 0], true),
+		PERMUTE.coordinates([2, 1, phi, phiinv], true),
+		].flat();
+	let i = 1;
+	for( const n of nodes ) {
+		n["id"] = i;
+		i++;
+	}
+	return nodes;
+}
+
+
+
+export const cell120 = () => {
+	const nodes  = make_120cell_vertices();
+
+	return {
+		nodes: nodes,
+		links: []
+	}
+}
+