Faces and stuff

permute_testbed.js

@@ -281,6 +281,85 @@ function make_120cell_vertices() {
 }
 
 
+
+// face detection for the 120-cell
+
+// NOTE: all of these return node ids, not nodes
+
+// return all the links which connect to a node
+
+function nodes_links(links, nodeid) {
+	return links.filter((l) => l.source === nodeid || l.target === nodeid);
+}
+
+// filter to remove a link to a given id from a set of links
+
+function not_to_this(link, nodeid) {
+	return !(link.source === nodeid || link.target === nodeid);
+}
+
+// given nodes n1, n2, return all neighbours of n2 which are not n1
+
+function unmutuals(links, n1id, n2id) {
+	const nlinks = nodes_links(links, n2id).filter((l) => not_to_this(l, n1id));
+	return nlinks.map((l) => {
+		if( l.source === n2id ) {
+			return l.target;
+		} else {
+			return l.source;
+		}
+	})
+}
+
+
+function fingerprint(ids) {
+	const sids = [...ids];
+	sids.sort();
+	return sids.join(',');
+}
+
+
+
+function auto_120cell_faces(links) {
+	const faces = [];
+	const seen = {};
+	let id = 1;
+	for( const edge of links ) {
+		const v1 = edge.source;
+		const v2 = edge.target;
+		const n1 = unmutuals(links, v2, v1);
+		const n2 = unmutuals(links, v1, v2);
+		const shared = [];
+		for( const a of n1 ) {
+			const an = unmutuals(links, v1, a);
+			for( const d of n2 ) {
+				const dn = unmutuals(links, v2, d);
+				for( const x of an ) {
+					for( const y of dn ) {
+						if( x == y ) {
+							shared.push([v1, a, x, d, v2])
+						}
+					}
+				}
+			}
+		}
+		if( shared.length !== 3 ) {
+			console.log(`Bad shared faces for ${edge.id} ${v1} ${v2}`);
+		}
+		for( const face of shared ) {
+			const fp = fingerprint(face);
+			if( !seen[fp] ) {
+				faces.push({ id: id, nodes: face });
+				id++;
+				seen[fp] = true;
+			}
+		}
+	}
+	return faces;
+}
+
+
+
 const cell120 = () => {
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
@@ -362,6 +441,8 @@ const cell600 = () => {
 }
 
 
+// bad stuff
+
 function find_chords(chords, n) {
 	return chords.filter((c) => c[0].id === n.id || c[1].id === n.id);
 }
@@ -661,8 +742,49 @@ function iterate_graph(nodes, links, n, fn) {
 }
 
 
-const nodes = make_120cell_vertices();
 
+
+// stupid tetrahedral labelling
+// keeps getting stuck
+
+
+function naive_label_120cell(nodes, links, n) {
+	const nodes_id = {};
+	nodes.map((n) => nodes_id[n.id] = n);
+	iterate_graph(nodes, links, nodes[0], (n) => {
+		const cols = new Set();
+		const nbors = find_adjacent(links, n.id);
+		for( const nb of nbors ) {
+			if( nodes_id[nb].label > 0 ) {
+				cols.add(nodes_id[nb].label);
+			}
+			for( const nb2 of find_adjacent(links, nb) ) {
+				if( nb2 !== n.id && nodes_id[nb].label > 0 ) {
+					cols.add(nodes_id[nb2].label);
+				}
+			}
+		}
+		const pcols = [ 1, 2, 3, 4, 5 ].filter((c) => !cols.has(c));
+		if( pcols.length < 1 ) {
+			console.log(`Got stuck, no options at ${n.id}`);
+			return false;
+		} else {
+			n.label = pcols[0];
+			console.log(`found ${pcols.length} colors for node ${n.id}`);
+			console.log(`applied ${pcols[0]} to node ${n.id}`);
+			return true;
+		}
+	});
+}
+
+
+
+
+
+
+
+
+const nodes = make_120cell_vertices();
 const links = auto_detect_edges(nodes, 4);
 
 

polytopes.js

@@ -360,6 +360,7 @@ function naive_label_120cell(nodes, links, n) {
 			return false;
 		} else {
 			n.label = pcols[0];
+			console.log(`found ${pcols.length} colors for node ${n.id}`);
 			console.log(`applied ${pcols[0]} to node ${n.id}`);
 			return true;
 		}
@@ -384,7 +385,6 @@ export const cell120 = () => {
 			node_size: 0.02,
 			link_size: 0.02
 		},
-		faces: faces
 	}
 }