diff --git a/cellindex.js b/cellindex.js
index 48838bb..4a07c10 100644
--- a/cellindex.js
+++ b/cellindex.js
@@ -105,12 +105,10 @@ export const LAYERS120 =  {
 };
 
 export const CELL120_CELL5 = {
-    "1": [ 258, 1, 510, 304, 431 ],
-    "2": [ 185, 93, 222, 295, 372 ],
+    "1": [ 1, 93, 37, 157 ],
 }
 
 
-
 // Schoute's partition via https://arxiv.org/abs/1010.4353
 
 export const PARTITION600 = {
diff --git a/explore_120cell.js b/explore_120cell.js
index 474d301..af0a0de 100644
--- a/explore_120cell.js
+++ b/explore_120cell.js
@@ -161,9 +161,9 @@ export function gather_5cells(cell120) {
 }
 
 function audit_5cells(cells) {
-    // this verifies that for each label (a 600-cell set), each of its 
+    // this verifies that for each label (a 600-cell set), each of its
     // vertices is in exactly 7 5-cells. It checks out.
-    
+
     ['1','2','3','4','5'].map((l) => {
         const sets = {};
         for( const cell of cells ) {
@@ -199,7 +199,6 @@ function try_120_5_cells_fails(cell120, cells, l) {
                     console.log("overlap");
                     console.log(c);
                     return true;
- 
                 }
             }
             return false;
@@ -269,27 +268,24 @@ function node_dist(cell120, aid, bid) {
     return dist(a, b);
 }
 
+function print_row(v1, v2, p, v5) {
+    console.log(`${v1.id},${v2.id},${p},${v5[1]},${v5[2]},${v5[3]},${v5[4]},${v5[5]}`);
+}
+
+// for a pair of vertices which are on the same inscribed 600 cell,
+// this returns all 7 pairs of 5-cells which contain v1 and v2 and
+// which are also evenly spaced (ie every pair of vertices on the
+// same 600-cell  is one edge apart)
 
 
-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 ) {
+function find_adjoining_5cells(cell120, all5, v1, v2) {
+    const DIST600 = round_dist(node_dist(cell120, v1.id, v2.id));
+    const v15s = all5.filter((c5) => c5[v1.label] === v1.id);
+    const v25s = all5.filter((c5) => c5[v2.label] === v2.id);
+    let p = 0;
+    const c5pairs = [];
+    for( const v5a of v15s ) {
+        for( const v5b of v25s ) {
             let match = true;
             const d = {};
             for( const label in v5a ) {
@@ -299,19 +295,35 @@ function follow_600(cell120, all5) {
                 }
             }
             if( match ) {
-                console.log("--- pair ---");
-                console.log(v5a);
-                console.log(v5b);
+                c5pairs.push([ v5a, v5b ]);
             }
         }
     }
+    return c5pairs;
 }
 
 
 
+function tetra_600_cell(cell120, all5) {
+    // find a tetrahedron on one of the 600-cells
+
+    const v1 = cell120.nodes[0];
+    const n600s = neighbours600(cell120, v1.id);
+    const v2id = n600s[0];
+    const n2600s = neighbours600(cell120, v2id);
+    // find mutual neighbours of the first two
+    const mutuals = n2600s.filter((nid) => nid != v2id && nid != v1.id && n600s.includes(nid));
+    // find mutuals which are mutuals of each other
+    const m0 = mutuals[0];
+    const mn = neighbours600(cell120, m0);
+    const mm = mn.filter((nid) => nid != m0 && mutuals.includes(nid));
+    return [ v1.id, v2id, m0, mm[0] ];
+}
 
 const cell120 = POLYTOPES.cell120_inscribed();
 const all5 = gather_5cells(cell120);
 
-follow_600(cell120, all5);
+const tetra = tetra_600_cell(cell120, all5);
+
+console.log(tetra);
 
diff --git a/polytopes.js b/polytopes.js
index dd1f328..cc26b25 100644
--- a/polytopes.js
+++ b/polytopes.js
@@ -473,14 +473,14 @@ export const cell120_inscribed_cell5 = () => {
 
         const links = [];
 
-	for( const p of [ 1, 2 ]) {
+/*	for( const p of [ 1, 2 ]) {
 		const nodes600 = nodes.filter((n) => n.label === p);
 		const links600 = auto_detect_edges(nodes600, 12);
 		links600.map((l) => l.label = p);
 		links.push(...links600);
 	}
 
-        for( const c5 in CELLINDEX.CELL120_CELL5 ) {
+*/        for( const c5 in CELLINDEX.CELL120_CELL5 ) {
             const nodes5 = nodes.filter((n) => CELLINDEX.CELL120_CELL5[c5].includes(n.id));
             const links5 = auto_detect_edges(nodes5, 4);
             links5.map((l) => l.label = 0);