More mucking around with colouring nodes

NOTES.md

@@ -1,26 +1,15 @@
 # NOTES
 
 
-New approach for the 5-cells:
+## Labelling the inscribed 600-cells in a 120-cell
 
-Pick a tetrahedron of an inscribed 600-cell with vertices A, B, C, D
+I want to apply the partition of the 600-cell into five 24-cells to the inscribed
-
+600-cells in the 120-cell, so that I can use this partition to colour the inscribed
-This gives pairs of vertices:
+5-cells - since each 5-cell has a vertex in each of the 600-cells, getting a
-
+partition for just one will be enough.
-AB
-AC
-AD
-BC
-BD
-CD
-
-Each of these gives rise to seven pairs of 5-cells which are on neighboring vertices
-of the 5 600-cells.
-
-Try enumerating these and inspecting them to find one or more coherent sets of four
-5-cells which lie on one tetrahedron from each of the 600-cells.
-
-(I expect there to be more than one, like how there are two ways to partition the
-120-cell vertices into 600-cells)
 
+The challenge is that the 600-cells in the 120-cell are rotated differently to the
+coordinates for the original 600-cell. And I don't have enough maths to line them up.
 
+What about - given one of the inscribed 600-cell, find all of the 24-cells? (there
+are 25 possible ones so sorting them out will be a pain)

explore_120cell.js

@@ -437,7 +437,7 @@ function coherent_5cells_r(cell120, all5, c5s, c50) {
 
 
 
-function coherent_5cells(cell120, all5d) {
+function coherent_5cells(cell120, all5) {
     // pick a starting point, collect coherent 5_cells, continue till
     // there aren't any new ones
 
@@ -515,5 +515,40 @@ function coherent_one_set() {
     console.log(JSON.stringify(idict, null, 2));
 }
 
+function cell120_csv() {
+    const cell120 = POLYTOPES.cell120_inscribed();
+    const coords = [ 'x', 'y', 'z', 'w' ];
+    console.log("id,label,x,y,z,w,zeroes");
+    for( const n of cell120.nodes ) {
+        const zc = coords.filter((c) => n[c] === 0);
+        console.log(`${n.id},${n.label},${n.x},${n.y},${n.z},${n.w},${zc.length}`);
+    }
+}
+
+
+function cell600_links(cell600, n) {
+    const links = cell600.links.filter((l) => l.source === n.id || l.target === n.id);
+    const nbors = links.map((l) => {
+        if( l.source === n.id ) {
+            return l.target;
+        } else {
+            return l.source;
+        }
+    });
+    return nbors.sort((a, b) => a - b);
+}
+
+
+function cell600_csv() {
+    const cell600 = POLYTOPES.cell600();
+    console.log("id,label,x,y,z,w,d");
+    const n0 = cell600.nodes[0];
+    for( const n of cell600.nodes ) {
+        const d = dist(n0, n);
+        const nbors = cell600_links(cell600, n);
+        const nids = nbors.join(',');
+        console.log(`${n.id},${n.label},${n.x},${n.y},${n.z},${n.w},${d},${nids}`);
+    }
+}
+cell600_csv();
 
-coherent_one_set();

gui.js

@@ -6,7 +6,7 @@ const DEFAULTS = {
 	nodeopacity: 1,
 	linksize: 1.0,
 	linkopacity: 0.75,
-	shape: '120-cell',
+	shape: '600-cell',
 	link2opacity: 0.75,
 	option: 'none',
 	visibility: 5,

polytopes.js

@@ -216,6 +216,7 @@ export const cell24 = () => {
 		links16.map((l) => l.label = p);
 		links.push(...links16);
 	}
+	// colour links `
 	// links.map((l) => {
 	// 	const ls = [ l.source, l.target ].map((nid) => node_by_id(nodes, nid).label);
 	// 	for ( const c of [1, 2, 3] ) {
@@ -348,6 +349,36 @@ export function make_120cell_vertices() {
 
 
 
+export function make_120cell_vertices_alt() {
+    // unit radius version to make it easier to partition one of the 600-cells
+	const phi = 0.5 * (1 + Math.sqrt(5));
+	const r5 = Math.sqrt(5);
+	const phi2 = phi * phi;
+	const phiinv = 1 / phi;
+	const phi2inv = 1 / phi2;
+	const r8 = Math.sqrt(8);
+	const p8 = phi / r8;
+	const r58 = r5 / r8;
+	const ir8 = 1 / r8;
+	const ip8 = phiinv / r8;
+	const p28 = phi2 / r8;
+	const ip28 = phi2inv / r8;
+
+	const nodes = [
+	    PERMUTE.coordinates([1, 0, 0, 0], 1),
+	    PERMUTE.coordinates([0.5, 0.5, 0.5, 0.5], 1),
+	    PERMUTE.coordinates([0, phiinv * 0.5, 0.5, phi * 0.5], 1, true),
+	    PERMUTE.coordinates([p8,  p8,  p8,  ip28], 0, true),
+	    PERMUTE.coordinates([ir8, ir8, ir8, r58], 0, true),
+	    PERMUTE.coordinates([ip8, ip8, ip8, p28], 0, true),
+	    PERMUTE.coordinates([0,   ip8, p8,  r58], 0, true),
+	    PERMUTE.coordinates([0,   ip28, ir8, p28], 0, true),
+	    PERMUTE.coordinates([ip8, ir8, p8, 2 * ir8], 0, true),
+	].flat();
+	index_nodes(nodes);
+	return nodes;
+}
+
 
 
 function label_nodes(nodes, ids, label) {
@@ -472,17 +503,28 @@ export const cell120_inscribed = () => {
 }
 
 
+export const cell120_alt = () => {
+	const nodes  = make_120cell_vertices_alt();
+	const links = auto_detect_edges(nodes, 4);
+
+	links.map((l) => l.label = 0);
+
+	return {
+		name: '120-cell-alt',
+		nodes: nodes,
+		links: links,
+		options: [
+			{ name: "none", links: [ 0 ]},
+	],
+		description: `alt 120-cell`,
+	}
+}
+
 
 export const cell120_inscribed_cell5 = () => {
 	const nodes  = make_120cell_vertices();
 	const links = [];
 
-  	for( const cstr in CELLINDEX.INDEX120 ) {
-		label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
-	}
-
-	links.map((l) => l.label = 0);
-
         const CELL5S = CELLINDEX.CELL120_CELL5.cell5s;
 
         for( const c5 in CELL5S ) {
@@ -490,6 +532,7 @@ export const cell120_inscribed_cell5 = () => {
             const links5 = auto_detect_edges(nodes5, 5);
             links5.map((l) => l.label = Number(c5));
             links.push(...links5);
+            nodes5.map((n) => n.label = Number(c5));
         }
 
         const show_links = Array.from({ length: 128 }, (_, i) => i);
@@ -549,7 +592,6 @@ export const cell120_inscribe_cell5_subset = () => {
 	        }
 	    }
         }
-        console.log(link5s);
 
 	return {
 		name: '120-cell 5-cell subset',
@@ -558,7 +600,7 @@ export const cell120_inscribe_cell5_subset = () => {
 		options: [
 			{ name: "none", links: [ 0, 1, 2, 3, 4, 5, 8 ]},
 		],
-		description: `Showing the subset of 5-cells in one icosahedron`,
+		description: `Showing only thirteen of the inscribed 5-cells and the links between them on the inscribed 600-cells`,
 	}
 }
 
@@ -695,7 +737,12 @@ 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
+        const plabels = {};
+
+	nodes.map((n) => {
+            plabels[n.id] = n.label;
+    	    n.label = 9
+	}); // make all invisible by default
 
 	for (const cstr in CELLINDEX.LAYERS600 ) {
 		label_nodes(nodes, CELLINDEX.LAYERS600[cstr], Number(cstr));
@@ -710,6 +757,12 @@ export const cell600_layered = () => {
 		}
 	});
 
+	// recolour nodes according to 24-cell partition
+
+        nodes.map((n) => n.label = 8 + plabels[n.id]); 
+
+        const node_c = [ 8, 9, 10, 11, 12, 13, 14, 15 ];
+
 	const options = [];
 	const layers = [];
 
@@ -718,7 +771,7 @@ export const cell600_layered = () => {
 		options.push({
 			name: CELLINDEX.LAYER_NAMES[i],
 			links: [...layers],
-			nodes: [...layers]
+			nodes: [...node_c, ...layers]
 		})
 	}
 
@@ -977,7 +1030,6 @@ export const build_all = () => {
 		cell600_layered(),
 	 	cell120_inscribed(),
 	 	cell120_inscribed_cell5(),
-	 	cell120_inscribe_cell5_subset(),
 	 	cell120_layered()
 	 	];
 }