From 137f7db0662f3e663e5e75d4b6b9ba12d0045be2 Mon Sep 17 00:00:00 2001
From: Mike Lynch <m.lynch@sydney.edu.au>
Date: Sun, 28 Dec 2025 18:05:42 +1100
Subject: [PATCH] Getting closer to an algorithm for the 120 5-cell inscription

---
 explore_120cell.js | 120 ++++++++++++++++++++++++++++++++++++++++++---
 1 file changed, 114 insertions(+), 6 deletions(-)

diff --git a/explore_120cell.js b/explore_120cell.js
index c30253d..474d301 100644
--- a/explore_120cell.js
+++ b/explore_120cell.js
@@ -1,10 +1,24 @@
 
+// TODO - try visualising the 5-cells from a vertex on the layered 120-cell
+// and get an intuition for how they work with the dodecahedral structure
+
+// Another new approach -
+// pick a starting 5-cell
+// look at the neighbours on the 120-cell of all of its 5 vertices
+// try to find abother 5-cell with these neighbours
+// if there's only one, add that to the list and keep going
+// if there's more than one, are they disjoint with each other?
 
 import * as POLYTOPES from './polytopes.js';
 
 // exploring more inscriptions of the 120-cell
 
 
+function choice(a) {
+    const r = Math.floor(Math.random() * a.length);
+    return a[r];
+}
+
 export function nodes_links(links, nodeid) {
     return links.filter((l) => l.source === nodeid || l.target === nodeid);
 }
@@ -166,11 +180,13 @@ function audit_5cells(cells) {
     });
 }
 
-function try_120_5_cells(cell120, cells, l) {
+function try_120_5_cells_fails(cell120, cells, l) {
     // iterate over every vertex in the 600-cell defined by label l,
     // get all 7 5-cells including that vertex, and add them if they are
     // disjoint with what we already have
 
+    // this always runs out of disjoint nodes early
+
     const vertices = cell120.nodes.filter((n) => n.label === l);
 
     const cellset = [];
@@ -179,13 +195,11 @@ function try_120_5_cells(cell120, cells, l) {
         const vcells = cells.filter((c) => c[l] === v.id);
         const overlap_any = (cs, c) => {
             for( const seen of cs ) {
-                console.log(c);
                 if( overlap(seen, c) ) {
                     console.log("overlap");
-                    console.log(seen);
                     console.log(c);
                     return true;
-                    
+ 
                 }
             }
             return false;
@@ -193,17 +207,111 @@ function try_120_5_cells(cell120, cells, l) {
         const disjoint = vcells.filter((c) => ! overlap_any(cellset, c));
         console.log(`Found ${disjoint.length} disjoint cells`);
         if( disjoint.length > 0 ) {
-            cellset.push(disjoint[0]);
+            cellset.push(choice(disjoint));
         }
     }
     console.log(`Found total of ${cellset.length} disjoint cells`);
     //console.log(cellset);
 }
 
+function overlap_any(cs, c) {
+    for( const seen of cs ) {
+        if( overlap(seen, c) ) {
+            return true;
+        }
+    }
+    return false;
+}
+
+
+function explore_disjoint(cell120, all5, l) {
+    const a = all5[0];
+
+    const overlaps = all5.filter((c) => overlap(c, a));
+
+    console.log(a);
+
+    console.log(overlaps.length);
+    console.log(overlaps);
+}
+
+// select a five-cell from a starting vertex v
+// find a neighbor of v vn on its 600 cell, find all of the 5-cells which include
+// vn. Then see if we can find any from that set which are similiar neighbours to 
+// the other four vertices in the first 5-cell 
+
+// the idea is that the 600-cells are a guide to finding the right subset of 
+// 5-cells 
+
+function neighbours600(cell120, vid) {
+    const v = cell120.nodes.filter((node) => node.id === vid)[0];
+    const label = v.label; 
+    const links = cell120.links.filter((l) => {
+        return l.label === v.label && (l.source === v.id || l.target == v.id );
+    });
+    const nodes = links.map((l) => {
+        if( l.source === v.id ) {
+            return l.target;
+        } else {
+            return l.source;
+        }
+    });
+    return nodes;
+}
+
+function cell120node(cell120, nid) {
+    return cell120.nodes.filter((n) => n.id === nid)[0];
+}
+
+function node_dist(cell120, aid, bid) {
+    const a = cell120node(cell120, aid);
+    const b = cell120node(cell120, bid);
+    return dist(a, b);
+}
+
+
+
+function follow_600(cell120, all5) {
+    const v = cell120.nodes[0];
+    console.log("Start vertex:");
+    console.log(v);
+    const v5s = all5.filter((c5) => c5[v.label] === v.id);
+    console.log(`Vertex ${v.id} belongs to these 5-cells:`);
+    console.log(v5s);
+    const n600s = neighbours600(cell120, v.id);
+    const n600id = n600s[0];
+    const n600 = cell120node(cell120, n600id); 
+    console.log("One 600-cell neighbour:");
+    console.log(n600);
+    const DIST600 = round_dist(node_dist(cell120, v.id, n600id));
+    const nv5s = all5.filter((c5) => c5[v.label] === n600id);
+    console.log(`Vertex ${n600id} belongs to these 5-cells:`); 
+    console.log(nv5s);
+    console.log("Distances for each pair of 5-cells from the two sets:");
+    for( const v5a of v5s ) {
+        for( const v5b of nv5s ) {
+            let match = true;
+            const d = {};
+            for( const label in v5a ) {
+                d[label] = round_dist(node_dist(cell120, v5a[label], v5b[label]));
+                if( d[label] != DIST600 ) {
+                    match = false;
+                }
+            }
+            if( match ) {
+                console.log("--- pair ---");
+                console.log(v5a);
+                console.log(v5b);
+            }
+        }
+    }
+}
+
 
 
 
 const cell120 = POLYTOPES.cell120_inscribed();
 const all5 = gather_5cells(cell120);
 
-try_120_5_cells(cell120, all5, 1);
+follow_600(cell120, all5);
+