Added indexing for tesseract

colours.js

@@ -3,7 +3,7 @@ import ColorScheme from 'color-scheme';
 export const get_colours = (basis) => {
 	const scheme = new ColorScheme;
 	const hexbasis = basis.toString(16).padStart(6, "0");
-	scheme.from_hex(hexbasis).scheme("analogic").variation("hard").distance(0.5);
+	scheme.from_hex(hexbasis).scheme("tetrade").variation("hard").distance(0.5);
 	return scheme.colors().map((cs) => parseInt('0x' + cs));
 }
 

main.js

@@ -33,6 +33,8 @@ scene.background = new THREE.Color(0x808080);
 const material = new THREE.MeshStandardMaterial({ color: 0x3293a9 });
 const node_colours = get_colours(0x3293a9);
 
+material.transparent = true;
+material.opacity = 0.5;
 
 const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c}));
 

permute_testbed.js

@@ -505,38 +505,42 @@ function make_120_partition(nodes, n) {
 	const pairs60 = neighbour_angles(chord3, n, "60.000");
 	const icosas = partition_nodes(pairs60);
 
+	n.label = 1;
 	const angles = icosa_nodes(nodes, icosas[0]);
 	label_120_partition_r(nodes, chord3, 1, n, angles);
 }
 
 // recursive function to label a single 600-cell vertex partition of the 
 // 120-cell by following icosahedral nets
+// this doesn't work! completely - labels only 108-112
 
 function label_120_partition_r(nodes, chords, label, origin, neighbours) {
-	console.log(`label_120_partition_r`);
+	console.log(`label_120_partition_r ${origin.id}`);
-	console.log(origin);
+	console.log(neighbours.map((n) => n.id).join(', '));
-	console.log(neighbours.map((n) => n.id));
+
+	// first try to label everything
+	const unlabelled = [];
 	for( const n of neighbours ) {
-
 		if( n.label === 0 ) {
+			console.log(`Labelled ${n.id} ${label}`);
 			n.label = label;
-			console.log(`Added ${n.id} to group ${label}`);
+			unlabelled.push(n);
-
+		} else if( n.label !== label ) {
-			// the angles represent two icosahedral pyramids - partition them and
+			console.log(`node ${n.id} is already in group ${n.label}`);
-			// pick the one which is at 60 to the edge we arrived on
+			//return false;
-			console.log(`looking for more neighbors for ${n}`);
-			const pairs60 = neighbour_angles(chords, n, "60.000");
-			const icosas = partition_nodes(pairs60);
-			const icosa = choose_icosa(nodes, origin, n, icosas);
-			const icosa_n = icosa_nodes(nodes, icosa);
-			return label_120_partition_r(nodes, chords, label, n, icosa_n);
-		} else {
-			if( n.label !== label ) {
-				console.log(`node ${n.id} is already in group ${n.label}`);
-				return false;
-			}
 		}
 	}
+	for( const n of unlabelled ) { 
+		// the angles represent two icosahedral pyramids - partition them and
+		// pick the one which is at 60 to the edge we arrived on
+		//console.log(`looking for more neighbors for ${n}`);
+		const pairs60 = neighbour_angles(chords, n, "60.000");
+		const icosas = partition_nodes(pairs60);
+		const icosa = choose_icosa(nodes, origin, n, icosas);
+		const icosa_n = icosa_nodes(nodes, icosa);
+		console.log(`recursing to ${nice_icosa(nodes,icosa)}`);
+		return label_120_partition_r(nodes, chords, label, n, icosa_n);
+	}
 }
 
 // given a pair of icosa-sets, pick the one which is at the right angle to
@@ -558,7 +562,7 @@ function choose_icosa(nodes, origin, n1, icosas) {
 }
 
 function icosa_nodes(nodes, icosa) {
-	return Array.from(icosa).map((nid) => node_by_id(nodes, nid));
+	return Array.from(icosa).map((nid) => node_by_id(nodes, nid)).sort((a, b) => a.id - b.id);
 }
 
 function node_by_id(nodes, nid) {
@@ -567,13 +571,64 @@ function node_by_id(nodes, nid) {
 }
 
 
+function enumerate_icosas(nodes) {
+	const chords = find_all_chords(nodes);
+	const chord3 = chords["1.74806"];  // these are edges of the 600-cells;
+
+	for( const n of nodes ) {
+		const pairs60 = neighbour_angles(chord3, n, "60.000");
+		const icosas = partition_nodes(pairs60);
+		for( const icosa of icosas ) {
+			const inodes = icosa_nodes(nodes, icosa);
+			console.log(icosa_to_csv(n.id, inodes).join(','));
+		}
+	}
+}
+
+
+function icosa_to_csv(nid, icosa) {
+	const cols = [ nid ];
+	const ia = icosa.map((n) => n.id);
+	for( let i = 1; i < 601; i++ ) {
+		if( ia.includes(i) ) {
+			cols.push(i);
+		} else {
+			cols.push('')
+		}
+	}
+	return cols;
+}
+
+
+function start_icosas(nodes, chords, origin) {
+	const pairs60 = neighbour_angles(chords, origin, "60.000");
+	return partition_nodes(pairs60).map((i) => nice_icosa(nodes, i));
+}
+
+
+
+function next_icosa(nodes, chords, origin, nid) {
+	const n = node_by_id(nodes, nid);
+	const pairs60 = neighbour_angles(chords, n, "60.000");
+	const icosas = partition_nodes(pairs60);
+	const icosa = choose_icosa(nodes, origin, n, icosas);
+
+	return nice_icosa(nodes, icosa);
+}
+
+function nice_icosa(nodes, icosa) {
+	return icosa_nodes(nodes, icosa).map((n) => n.id).join(', ');
+}
+
 
 const nodes = make_120cell_vertices();
-
 // const chords = find_all_chords(nodes);
 // const chord3 = chords["1.74806"];  // these are edges of the 600-cells;
-// const pairs60 = neighbour_angles(chord3, nodes[0], "60.000");
+
-// const icosas = partition_nodes(pairs60);
+//const pairs60 = neighbour_angles(chord3, nodes[0], "60.000");
+//const icosas = partition_nodes(pairs60);
+
+make_120_partition(nodes, nodes[0])
 
 
 

polytopes.js

@@ -119,6 +119,13 @@ export const cell16 = () => {
 export const tesseract = () => {
 	const nodes = PERMUTE.coordinates([1, 1, 1, 1],  0);
 	index_nodes(nodes);
+
+	for( const n of nodes ) {
+		if( n.x * n.y * n.z * n.w > 0 ) {
+			n.label = 1;
+		}
+	}
+
 	scale_nodes(nodes, Math.sqrt(2) / 2);
 	const links = auto_detect_edges(nodes, 4);
 
@@ -168,6 +175,7 @@ export const cell24 = () => {
 // see table in https://en.wikipedia.org/wiki/120-cell - maybe adapt the
 // unit radius table
 
+
 function make_120cell_vertices() {
 	const phi = 0.5 * (1 + Math.sqrt(5));  
 	const r5 = Math.sqrt(5);   
@@ -177,23 +185,21 @@ function make_120cell_vertices() {
 
 	const nodes = [
 		PERMUTE.coordinates([0, 0, 2, 2],  0),
-		PERMUTE.coordinates([1, 1, 1, r5], 0),
+		PERMUTE.coordinates([1, 1, 1, r5], 1),
-		PERMUTE.coordinates([phi, phi, phi, phi2inv], 0),
+		PERMUTE.coordinates([phi, phi, phi, phi2inv], 2),
-		PERMUTE.coordinates([phiinv, phiinv, phiinv, phi2], 0),
+		PERMUTE.coordinates([phiinv, phiinv, phiinv, phi2], 3),
 
-		PERMUTE.coordinates([phi2, phi2inv, 1, 0], 0, true),
+		PERMUTE.coordinates([phi2, phi2inv, 1, 0], 4, true),
-		PERMUTE.coordinates([r5, phiinv, phi, 0], 0, true),
+		PERMUTE.coordinates([r5, phiinv, phi, 0], 5, true),
-		PERMUTE.coordinates([2, 1, phi, phiinv], 0, true),
+		PERMUTE.coordinates([2, 1, phi, phiinv], 6, true),
 		].flat();
 	index_nodes(nodes);
-	label_nodes(nodes, [1], 1);
-	label_nodes(nodes, [25, 41, 97, 109, 157, 161, 173, 177, 113, 37, 53, 93 ], 2);
-
-	label_nodes(nodes, [29, 45, 101, 105, 153, 165, 169, 181, 117, 33, 49, 89], 4);
 	scale_nodes(nodes, 0.5);
 	return nodes;
 }
 
+
+
 function label_nodes(nodes, ids, label) {
 	nodes.filter((n) => ids.includes(n.id)).map((n) => n.label = label);
 }