cellindex.js

@@ -1,4 +1,17 @@
-export const INDEX = {
+
+export const LAYER_NAMES = {
+	0: "North pole",
+	1: "Arctic circle",
+	2: "North temperate",
+	3: "Tropic of Cancer",
+	4: "Equator",
+	5: "Tropic of Capricorn",
+	6: "South temperate",
+	7: "Antarctic circle (all)"
+};
+
+
+export const INDEX120 = {
 	"1": [
 		27,38,48,49,61,68,74,87,95,98,105,120, 126,131,140,149,156,165,174,
 		179,185,200,207,210,218,223,226,231,234,239,241,248,252,253,258,263,
@@ -46,7 +59,7 @@ export const INDEX = {
 };
 
 
-export const LAYERS =  {
+export const LAYERS120 =  {
 	"0": [154,266,158,222,218,250,254,162,268,156,160,252,256,166,270,272,
 		164,220,224,168],
 	"1": [2,318,314,30,414,510,362,26,506,410,338,458,462,110,
@@ -90,3 +103,86 @@ export const LAYERS =  {
 	"7":[217,153,221,157,265,161,165,269,249,253,251,255,267,159,155,
 		163,219,271,223,167]
 };
+
+// Schoute's partition via https://arxiv.org/abs/1010.4353
+
+export const PARTITION600 = {
+
+	"2,0,0,0": 1,
+	"0,2,0,0": 1,
+	"0,0,2,0": 1,
+	"0,0,0,2": 1,
+	"1,1,1,1": 1,
+	"1,1,-1,-1": 1,
+	"1,-1,1,-1": 1,
+	"1,-1,-1,1": 1,
+	"1,-1,-1,-1": 1,
+	"1,-1,1,1": 1,
+	"1,1,-1,1": 1,
+	"1,1,1,-1": 1,
+
+	"k,0,-t,-1": 2,
+	"0,k,1,-t": 2,
+	"t,-1,k,0": 2,
+	"1,t,0,k": 2,
+	"t,k,0,-1": 2,
+	"1,0,k,t": 2,
+	"k,-t,-1,0": 2,
+	"0,1,-t,k": 2,
+	"1,k,t,0": 2,
+	"t,0,-1,k": 2,
+	"0,t,-k,-1": 2,
+	"k,-1,0,-t": 2,
+
+	"t,0,1,k": 3,
+	"0,t,-k,1": 3,
+	"1,-k,-t,0": 3,
+	"k,1,0,-t": 3,
+	"0,k,1,t": 3,
+	"t,1,-k,0": 3,
+	"k,0,t,-1": 3,
+	"1,-t,0,k": 3,
+	"t,-k,0,-1": 3,
+	"0,1,-t,-k": 3,
+	"1,0,-k,t": 3,
+	"k,t,1,0": 3,
+
+	"t,0,-1,-k": 4,
+	"0,t,k,-1": 4,
+	"1,-k,t,0": 4,
+	"k,1,0,t": 4,
+	"t,1,k,0": 4,
+	"0,k,-1,-t": 4,
+	"1,-t,0,-k": 4,
+	"k,0,-t,1": 4,
+	"0,1,t,k": 4,
+	"t,-k,0,1": 4,
+	"k,t,-1,0": 4,
+	"1,0,k,-t": 4,
+
+	"k,0,t,1": 5,
+	"0,k,-1,t": 5,
+	"t,-1,-k,0": 5,
+	"1,t,0,-k": 5,
+	"1,0,-k,-t": 5,
+	"t,k,0,1": 5,
+	"0,1,t,-k": 5,
+	"k,-t,1,0": 5,
+	"t,0,1,-k": 5,
+	"1,k,-t,0": 5,
+	"k,-1,0,t": 5,
+	"0,t,k,1": 5
+};
+
+
+
+export const LAYERS600 = {
+	"0":[2,42,46,50,54,106,110,44,48,52,56,108,112],
+	"1":[10,12,14,16,18,20,22,24,34,36,38,40,98,102,100,104,90,92,94,96],
+	"2":[26,58,74,28,76,30,60,32,62,78,80,64],
+	"3":[3,4,5,6,7,8,65,113,81,66,114,82,67,115,83,68,116,84,69,117,85,70,118,86,71,119,87,72,120,88],
+	"4":[25,29,27,31,57,61,59,63,73,75,77,79],
+	"5":[97,101,99,103,33,35,37,39,89,91,93,95,9,11,13,15,17,19,21,23],
+	"6":[41,105,49,43,51,45,107,47,109,53,55,111],
+	"7":[1]
+};

layer600cell.js

@@ -0,0 +1,173 @@
+
+
+import * as POLYTOPES from './polytopes.js';
+
+// face detection for the 600-cell
+
+
+export function nodes_links(links, nodeid) {
+	return links.filter((l) => l.source === nodeid || l.target === nodeid);
+}
+
+
+export function linked(links, n1, n2) {
+	const ls = nodes_links(nodes_links(links, n1), n2);
+	if( ls.length ) {
+		return ls[0]
+	} else {
+		return false;
+	}
+}
+
+
+function fingerprint(ids) {
+	const sids = [...ids];
+	sids.sort();
+	return sids.join(',');
+}
+
+
+export function make_600cell() {
+	const nodes = POLYTOPES.make_600cell_vertices();
+	const links = POLYTOPES.auto_detect_edges(nodes, 12);
+	return {
+		nodes: nodes,
+		links: links
+	}
+}
+
+export function link_to_tetras(nodes, links, link) {
+	const n1 = link.source;
+	const n2 = link.target;
+	const nl1 = nodes_links(links, n1).filter((l) => l.id !== link.id);
+	const nl2 = nodes_links(links, n2).filter((l) => l.id !== link.id);
+	const p1 = new Set();
+	const p = new Set();
+	for( const nl of nl1 ) {
+		if( nl.source !== n1 ) {
+			p1.add(nl.source);
+		}
+		if( nl.target !== n1 ) {
+			p1.add(nl.target);
+		}
+	}
+	for( const nl of nl2 ) {
+		if( nl.source !== n2 && p1.has(nl.source) ) {
+			p.add(nl.source);
+		}
+		if( nl.target !== n2 && p1.has(nl.target) ) {
+			p.add(nl.target);
+		}
+	}
+	const lp = Array.from(p);
+	const seen = {};
+	const tetras = [];
+	for( const p1 of lp ) {
+		for( const p2 of lp ) {
+			if( p1 != p2 ) {
+				if( linked(links, p1, p2) ) {
+					const fp = fingerprint([n1, n2, p1, p2]);
+					if( !seen[fp] ) {
+						seen[fp] = true;
+						tetras.push({fingerprint: fp, nodes: [n1, n2, p1, p2]})
+					}
+				}
+			}
+		}
+	}
+	return tetras;
+}
+
+
+export function auto_600cell_cells(nodes, links) {
+	const seen = {};
+	const tetras = [];
+	links.map((link) => {
+		link_to_tetras(nodes, links, link).map((lt) => {
+			if( !seen[lt.fingerprint] ) {
+				seen[lt.fingerprint] = true;
+				tetras.push(lt.nodes);
+			}
+		})
+	});
+
+	return tetras;
+}
+
+
+function node_by_id(nodes, nid) {
+	const ns = nodes.filter((n) => n.id === nid);
+	return ns[0];
+}
+
+
+export function tetra_w(nodes, tetra) {
+	let w = 0;
+	for( const nid of tetra ) {
+		const node = node_by_id(nodes, nid);
+		w += node.w;
+	}
+	return w / 4;
+}
+
+export function sorted_600cells() {
+	const cell600 = make_600cell();
+	const tetras = auto_600cell_cells(cell600.nodes, cell600.links);
+	const layers = tetras.map((t) => { return { "nodes": t, w: tetra_w(cell600.nodes, t) } });
+	layers.sort((a, b) => b.w - a.w);
+	return layers;
+}
+
+// const cell600 = make_600cell();
+
+// const layers = sorted_600cells(cell600.nodes, cell600.links);
+// for( const cell of layers ) {
+// //	const fp = fingerprint(cell.nodes);
+// 	console.log(`${cell.w} ${cell.nodes}`);
+// }
+
+export function make_layered_600cell() {
+	const tetras = sorted_600cells()
+
+	const LAYERS = [
+		[ "00", 20 ],
+		[ "01", 20 ], 
+		[ "02", 30 ], 
+		[ "03", 60 ], 
+		[ "04", 60 ], 
+		[ "05", 60 ], 
+		[ "06", 20 ],
+		[ "07", 60 ], 
+		[ "08", 20 ],
+		[ "09", 60 ], 
+		[ "10", 60 ], 
+		[ "11", 60 ], 
+		[ "12", 30 ], 
+		[ "13", 20 ], 
+		[ "14", 20 ]
+	];
+
+	const vertices = {};
+	const seen = {};
+	let i = 0;
+
+	for( const layer of LAYERS ) {
+		const label = layer[0];
+		const n = layer[1];
+		vertices[label] = [];
+		console.log(`Layer ${label} starting at ${i}`);
+		for( const t of tetras.slice(i, i + n) ) {
+			console.log(t);
+			for( const n of t.nodes ) {
+				if( !seen[n] ) {
+					vertices[label].push(n);
+					seen[n] = true;
+				}
+			}
+		}
+		i += n;
+	}
+	return JSON.stringify(vertices);
+}
+
+

polytopes.js

@@ -1,6 +1,6 @@
 import * as PERMUTE from './permute.js';
 
-import * as CELL120 from './cellindex.js';
+import * as CELLINDEX from './cellindex.js';
 
 function index_nodes(nodes, scale) {
 	let i = 1;
@@ -22,7 +22,7 @@ function dist2(n1, n2) {
 	return (n1.x - n2.x) ** 2 + (n1.y - n2.y) ** 2 + (n1.z - n2.z) ** 2 + (n1.w - n2.w) ** 2;
 }
 
-function auto_detect_edges(nodes, neighbours, debug=false) {
+export function auto_detect_edges(nodes, neighbours, debug=false) {
 	const seen = {};
 	const nnodes = nodes.length;
 	const links = [];
@@ -359,23 +359,13 @@ function link_labels(nodes, link) {
 // layer and the links follow that
 
 export const cell120_layered = (max) => {
-	const LAYER_NAMES = {
-		0: "North pole",
-		1: "Arctic circle",
-		2: "North temperate",
-		3: "Tropic of Cancer",
-		4: "Equator",
-		5: "Tropic of Capricorn",
-		6: "South temperate",
-		7: "Antarctic circle (all)"
-	};
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
 
 	nodes.map((n) => n.label = 9); // make all invisible by default
 
-	for (const cstr in CELL120.LAYERS ) {
+	for (const cstr in CELLINDEX.LAYERS120 ) {
-		label_nodes(nodes, CELL120.LAYERS[cstr], Number(cstr));
+		label_nodes(nodes, CELLINDEX.LAYERS120[cstr], Number(cstr));
 	}
 
 	links.map((l) => {
@@ -393,7 +383,7 @@ export const cell120_layered = (max) => {
 	for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
 		layers.push(i);
 		options.push({
-			name: LAYER_NAMES[i],
+			name: CELLINDEX.LAYER_NAMES[i],
 			links: [...layers],
 			nodes: [...layers]
 		})
@@ -419,8 +409,8 @@ export const cell120_inscribed = () => {
 	const nodes  = make_120cell_vertices();
 	const links = auto_detect_edges(nodes, 4);
 
-  	for( const cstr in CELL120.INDEX ) {
+  	for( const cstr in CELLINDEX.INDEX120 ) {
-		label_nodes(nodes, CELL120.INDEX[cstr], Number(cstr));
+		label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
 	}
 
 	links.map((l) => l.label = 0);
@@ -450,76 +440,6 @@ export const cell120_inscribed = () => {
 
 
 
-// Schoute's partition via https://arxiv.org/abs/1010.4353
-
-const partition600 = {
-
-	"2,0,0,0": 1,
-	"0,2,0,0": 1,
-	"0,0,2,0": 1,
-	"0,0,0,2": 1,
-	"1,1,1,1": 1,
-	"1,1,-1,-1": 1,
-	"1,-1,1,-1": 1,
-	"1,-1,-1,1": 1,
-	"1,-1,-1,-1": 1,
-	"1,-1,1,1": 1,
-	"1,1,-1,1": 1,
-	"1,1,1,-1": 1,
-
-	"k,0,-t,-1": 2,
-	"0,k,1,-t": 2,
-	"t,-1,k,0": 2,
-	"1,t,0,k": 2,
-	"t,k,0,-1": 2,
-	"1,0,k,t": 2,
-	"k,-t,-1,0": 2,
-	"0,1,-t,k": 2,
-	"1,k,t,0": 2,
-	"t,0,-1,k": 2,
-	"0,t,-k,-1": 2,
-	"k,-1,0,-t": 2,
-
-	"t,0,1,k": 3,
-	"0,t,-k,1": 3,
-	"1,-k,-t,0": 3,
-	"k,1,0,-t": 3,
-	"0,k,1,t": 3,
-	"t,1,-k,0": 3,
-	"k,0,t,-1": 3,
-	"1,-t,0,k": 3,
-	"t,-k,0,-1": 3,
-	"0,1,-t,-k": 3,
-	"1,0,-k,t": 3,
-	"k,t,1,0": 3,
-
-	"t,0,-1,-k": 4,
-	"0,t,k,-1": 4,
-	"1,-k,t,0": 4,
-	"k,1,0,t": 4,
-	"t,1,k,0": 4,
-	"0,k,-1,-t": 4,
-	"1,-t,0,-k": 4,
-	"k,0,-t,1": 4,
-	"0,1,t,k": 4,
-	"t,-k,0,1": 4,
-	"k,t,-1,0": 4,
-	"1,0,k,-t": 4,
-
-	"k,0,t,1": 5,
-	"0,k,-1,t": 5,
-	"t,-1,-k,0": 5,
-	"1,t,0,-k": 5,
-	"1,0,-k,-t": 5,
-	"t,k,0,1": 5,
-	"0,1,t,-k": 5,
-	"k,-t,1,0": 5,
-	"t,0,1,-k": 5,
-	"1,k,-t,0": 5,
-	"k,-1,0,t": 5,
-	"0,t,k,1": 5
-};
-
 
 
 function partition_coord(i, coords, invert) {
@@ -560,7 +480,7 @@ function map_coord(i, coords, values) {
 }
 
 
-function make_600cell_vertices() {
+export function make_600cell_vertices() {
 	const coords = {
 		0: '0',
 		1: '1',
@@ -584,7 +504,7 @@ function make_600cell_vertices() {
 	].flat();
 
 	for( const n of nodes ) {
-		n.label = label_vertex(n, coords, partition600);
+		n.label = label_vertex(n, coords, CELLINDEX.PARTITION600);
 	}
 
 	for( const n of nodes ) {
@@ -649,6 +569,60 @@ export const cell600 = () => {
 	}
 }
 
+
+export const cell600_layered = () => {
+	const nodes  = make_600cell_vertices();
+	const links = auto_detect_edges(nodes, 12);
+
+	nodes.map((n) => n.label = 9); // make all invisible by default
+
+	for (const cstr in CELLINDEX.LAYERS600 ) {
+		label_nodes(nodes, CELLINDEX.LAYERS600[cstr], Number(cstr));
+	}
+
+	links.map((l) => {
+		const labels = link_labels(nodes, l);
+		if( labels[0] >= labels[1] ) {
+			l.label = labels[0];
+		} else {
+			l.label = labels[1];
+		}
+	});
+
+	const options = [];
+	const layers = [];
+
+	for( const i of [ 0, 1, 2, 3, 4, 5, 6, 7 ] ) {
+		layers.push(i);
+		options.push({
+			name: CELLINDEX.LAYER_NAMES[i],
+			links: [...layers],
+			nodes: [...layers]
+		})
+	}
+
+	return {
+		name: '600-cell layered',
+		nodes: nodes,
+		links: links,
+		geometry: {
+			node_size: 0.02,
+			link_size: 0.02
+		},
+		nolink2opacity: true,
+		options: options
+	}
+
+
+}
+
+
+
+
+
+
+
+
 function make_dodecahedron_vertices() {
 	const phi = 0.5 * (1 + Math.sqrt(5));  
 	const phiinv = 1 / phi;    
@@ -721,6 +695,7 @@ export const build_all = () => {
 		tesseract(),
 		cell24(),
 		cell600(),
+		cell600_layered(),
 	 	cell120_inscribed(),
 	 	cell120_layered()
 	 	];