More explorations of the 120-cell's 5-cells

CHANGELOG.md

@@ -1,12 +1,7 @@
 CHANGELOG
 =========
 
-## v1.2 - 18/1/2026
-
-Added a second visualisation of the 120-cell's 5-cells without the 120-cell links
-and with more colours added so you can get a sense of the individual 5-cells.
-
-## v1.1 - 1/1/2026
+## v1.1 - 1/1/2025
 
 The 120-cell now includes a visualisation of its inscribed 5-cells, which honestly
 looks like less of a mess than I expected it to.

cellindex.js

@@ -949,6 +949,100 @@ export const CELL120_CELL5 = {
     541
   ]
    },
+   "some_cell5s": {
+  "1": [
+    27,
+    28,
+    264,
+    309,
+    275
+  ],
+  "2": [
+    223,
+    76,
+    238,
+    84,
+    225
+  ],
+  "3": [
+    253,
+    44,
+    283,
+    304,
+    42
+  ],
+  "4": [
+    419,
+    112,
+    197,
+    578,
+    521
+  ],
+  "5": [
+    339,
+    14,
+    384,
+    382,
+    337
+  ],
+  "6": [
+    331,
+    4,
+    335,
+    390,
+    386
+  ],
+  "7": [
+    427,
+    160,
+    551,
+    146,
+    557
+  ],
+  "8": [
+    265,
+    60,
+    64,
+    295,
+    246
+  ],
+  "9": [
+    473,
+    100,
+    495,
+    213,
+    462
+  ],
+  "10": [
+    393,
+    6,
+    328,
+    397,
+    326
+  ],
+  "11": [
+    539,
+    164,
+    439,
+    561,
+    142
+  ],
+  "12": [
+    511,
+    122,
+    456,
+    595,
+    181
+  ],
+  "13": [
+    555,
+    154,
+    152,
+    545,
+    429
+  ]
+}
+
 
 };
 

colours.js

@@ -9,11 +9,12 @@ export const get_colours = (basis) => {
 	const luminance = hslb['color'][2];
 	const scheme = new ColorScheme;
 	scheme.from_hue(hue).scheme("tetrade").distance(0.75);
-	const scolours = scheme.colors();
-	const colours = [ ...scolours,  ...scolours, ...scolours, ...scolours, ...scolours,  ...scolours, ...scolours, ...scolours ]; 
+	const colours = scheme.colors().slice(1, 9);
+	colours.reverse();
 	const hsl = colours.map((c) => Color("#" + c).hsl());
 	const resaturated = hsl.map((hslc) => hslc.saturationl(saturation).rgbNumber()); 
 	resaturated.unshift(basis);
+	console.log(resaturated);
 	return resaturated;
 }
 

explore_120cell.js

@@ -437,7 +437,7 @@ function coherent_5cells_r(cell120, all5, c5s, c50) {
 
 
 
-function coherent_5cells(cell120, all5) {
+function coherent_5cells(cell120, all5d) {
     // pick a starting point, collect coherent 5_cells, continue till
     // there aren't any new ones
 
@@ -452,41 +452,68 @@ function coherent_5cells(cell120, all5) {
 
 
 
+function coherent_all() {
 
 
+    const cell120 = POLYTOPES.cell120_inscribed();
+    const all5 = gather_5cells(cell120);
 
-const cell120 = POLYTOPES.cell120_inscribed();
-const all5 = gather_5cells(cell120);
+    const c5s = coherent_5cells(cell120, all5);
 
-const c5s = coherent_5cells(cell120, all5);
-
-const celli = c5s.map((c5) => [ "1", "2", "3", "4", "5" ].map((l) => c5[l]));
+    const celli = c5s.map((c5) => [ "1", "2", "3", "4", "5" ].map((l) => c5[l]));
 
 
-// check it because I don't believe it yet
+    // check it because I don't believe it yet
 
-const vertex_check = {};
+    const vertex_check = {};
 
-for( const c5 of celli ) {
-    for( const l in c5 ) {
-        const v = c5[l];
-        if( v in vertex_check ) {
-            console.log(`Double count vertex ${v}`);
+    for( const c5 of celli ) {
+        for( const l in c5 ) {
+            const v = c5[l];
+            if( v in vertex_check ) {
+                console.log(`Double count vertex ${v}`);
+            }
+            vertex_check[v] = 1;
         }
-        vertex_check[v] = 1;
     }
-}
 
-for( let i = 1; i < 601; i++ ) {
-    if( !vertex_check[i] ) {
-       console.log(`v ${i} missing`);
+    for( let i = 1; i < 601; i++ ) {
+        if( !vertex_check[i] ) {
+           console.log(`v ${i} missing`);
+        }
     }
+
+
+    const idict = {};
+    for( let i = 1; i < 121; i++ ) {
+        idict[i] = celli[i - 1];
+    }
+
+    console.log(JSON.stringify(idict, null, 2));
 }
 
 
-const idict = {};
-for( let i = 1; i < 121; i++ ) {
-    idict[i] = celli[i - 1];
+
+function coherent_one_set() {
+
+
+    const cell120 = POLYTOPES.cell120_inscribed();
+    const all5 = gather_5cells(cell120);
+
+    const c5ns = cell5_tetras(cell120, all5, all5[0]);
+
+
+    const celli = c5ns.map((c5) => [ "1", "2", "3", "4", "5" ].map((l) => c5[l]));
+
+
+    const idict = {};
+
+    for( let i = 0; i < celli.length; i++ ) {
+       idict[i + 1] = celli[i];
+    }
+
+    console.log(JSON.stringify(idict, null, 2));
 }
 
-console.log(JSON.stringify(idict, null, 2));
+
+coherent_one_set();

index.html

@@ -36,7 +36,7 @@
 		<script type="module" src="/main.js"></script>
 		<div id="description"></div>
 		<div id="release_notes"></div>
-		<div id="info"><a href="#" id="show_notes">release 1.2</a> |
+		<div id="info"><a href="#" id="show_notes">release 1.1</a> |
 
     		by <a target="_blank" href="https://mikelynch.org/">Mike Lynch</a> |
 			<a target="_blank" href="https://git.tilde.town/bombinans/fourdjs">source</a></div>

main.js

@@ -1,15 +1,6 @@
 import * as THREE from 'three';
 
 const RELEASE_NOTES = `
-<p><b>v1.2 - 18/1/2026</b></p>
-
-<p>Added a second visualisation of the 120-cell's 5-cells without the 120-cell links and with more colours added so you can get a sense of the individual 5-cells.</p>
-
-<p><b>v1.1 - 1/1/2026</b></p>
-
-<p>The 120-cell now includes a visualisation of its inscribed 5-cells, which honestly
-looks like less of a mess than I expected it to.</p>
-
 <p><b>v1.0 - 16/11/2025</b></p>
 
 <p>It's been <a target="_blank" href="https://mikelynch.org/2023/Sep/02/120-cell/">two years</a> since

polytopes.js

@@ -475,7 +475,7 @@ export const cell120_inscribed = () => {
 
 export const cell120_inscribed_cell5 = () => {
 	const nodes  = make_120cell_vertices();
-	const links = [];
+	const links = auto_detect_edges(nodes, 4);
 
   	for( const cstr in CELLINDEX.INDEX120 ) {
 		label_nodes(nodes, CELLINDEX.INDEX120[cstr], Number(cstr));
@@ -483,29 +483,76 @@ export const cell120_inscribed_cell5 = () => {
 
 	links.map((l) => l.label = 0);
 
-        const CELL5S = CELLINDEX.CELL120_CELL5.cell5s;
 
-        for( const c5 in CELL5S ) {
-            const nodes5 = nodes.filter((n) => CELL5S[c5].includes(n.id));
-            const links5 = auto_detect_edges(nodes5, 5);
-            links5.map((l) => l.label = Number(c5));
-            links.push(...links5);
-        }
 
-        const show_links = Array.from({ length: 128 }, (_, i) => i);
 
 	return {
-		name: '120 5-cells',
+		name: '120-cell-5-cell',
 		nodes: nodes,
 		links: links,
 		options: [
-			{ name: "none", links: show_links},
-	        ],
-		description: `The 120 5-cells from the 120-cell, without the latter's links. This colouring is pretty arbitrary, being based on the algorithm which partitioned the nodes: a later version will have something that's based on the symmetries of the 600-cells which each of the 5-cells has its nodes in.`,
+		    { name: "5-cells", links: [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ] },
+		],
+		description: `The 120-cell with one of its 5-cells.`,
 	}
 }
 
 
+export const cell120_inscribe_cell5_subset = () => {
+	const nodes  = make_120cell_vertices();
+	const links = auto_detect_edges(nodes, 4);
+
+  	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.some_cell5s;
+        const link5s = [];
+        const nodes_subset = [];
+
+        for( const c5 in CELL5S ) {
+            const nodes5 = nodes.filter((n) => CELL5S[c5].includes(n.id));
+            const cell5links = auto_detect_edges(nodes5, 5);
+            cell5links.map((l) => l.label = 8);
+            link5s.push(...cell5links);
+            for( const n5 of nodes5 ) {
+               nodes_subset.push(n5);
+            }
+        }
+
+        // now add the links of the inscribed 600-cells which have the 
+        // node subset in them 
+
+        const link_subset = (l) => {
+            const source = nodes_subset.filter((n) => n.id === l.source);
+            const target = nodes_subset.filter((n) => n.id === l.target);
+            return source.length === 1 && target.length === 1;
+        };
+
+	for( const p of [ 1, 2, 3, 4, 5 ]) {
+	    const nodes600 = nodes.filter((n) => n.label === p);
+	    const links600 = auto_detect_edges(nodes600, 12);
+    	    links600.map((l) => l.label = p);
+	    for( const link of links600 ) {
+    	        if( link_subset(link) ) {
+	            link5s.push(link);
+	        }
+	    }
+        }
+        console.log(link5s);
+
+	return {
+		name: '120-cell 5-cell subset',
+		nodes: nodes_subset,
+		links: link5s,
+		options: [
+			{ name: "none", links: [ 0, 1, 2, 3, 4, 5, 8 ]},
+		],
+		description: `Showing the subset of 5-cells in one icosahedron`,
+	}
+}
 
 function partition_coord(i, coords, invert) {
 	const j = invert ? -i : i;
@@ -922,6 +969,7 @@ export const build_all = () => {
 		cell600_layered(),
 	 	cell120_inscribed(),
 	 	cell120_inscribed_cell5(),
+	 	cell120_inscribe_cell5_subset(),
 	 	cell120_layered()
 	 	];
 }