diff --git a/fourDShape.js b/fourDShape.js
index c760d3f..32cfb78 100644
--- a/fourDShape.js
+++ b/fourDShape.js
@@ -6,13 +6,15 @@ const HYPERPLANE = 2.0;
 
 class FourDShape extends THREE.Group {
 
-	constructor(node_ms, link_ms, structure) {
+	constructor(node_ms, link_ms, face_ms, structure) {
 		super();
 		this.node_ms = node_ms;
 		this.link_ms = link_ms;
+		this.face_ms = face_ms;
 		this.nodes4 = structure.nodes;
 		this.nodes3 = {};
 		this.links = structure.links;
+		this.faces = ( "faces" in structure ) ? structure.faces : [];
 		this.node_size = structure.geometry.node_size;
 		this.link_size = structure.geometry.link_size;
 		this.node_scale = 1;
@@ -71,6 +73,32 @@ class FourDShape extends THREE.Group {
 		link.object.children[0].rotation.x = Math.PI / 2.0;
 	}
 
+
+	setFaceGeometry(face, geometry) {
+		const values = [];
+		for( const f of face.nodes ) {
+			const v3 = this.nodes3[f].v3;
+			values.push(v3.x);
+			values.push(v3.y);
+			values.push(v3.z);
+		}
+		const v3 = this.nodes3[face.nodes[0]].v3;
+		values.push(v3.x);
+		values.push(v3.y);
+		values.push(v3.z);
+		const vertices = new Float32Array(values);
+		geometry.setAttribute( 'position', new THREE.BufferAttribute( vertices, 3 ) );
+	}
+
+	makeFace(material, face) {
+		const geometry = new THREE.BufferGeometry();
+		this.setFaceGeometry(face, geometry)
+		const mesh = new THREE.Mesh( geometry, material );
+		this.add(mesh);
+		return mesh;
+	}
+
+
 	fourDtoV3(x, y, z, w, rotations) {
 		const v4 = new THREE.Vector4(x, y, z, w);
 		for ( const m4 of rotations ) {
@@ -94,6 +122,10 @@ class FourDShape extends THREE.Group {
 			const material = this.getMaterial(l, this.link_ms);
 			l.object = this.makeLink(material, l);
 		}
+		for( const f of this.faces ) {
+			const material = this.getMaterial(f, this.face_ms);
+			f.object = this.makeFace(material, f);
+		}
 	}
 
 
@@ -109,9 +141,13 @@ class FourDShape extends THREE.Group {
 		for( const l of this.links ) {
 			this.updateLink(l);
 		}
+
+		for( const f of this.faces ) {
+			this.setFaceGeometry(f, f.object.geometry);
+		}
 	}
 
 
 }
 
-export { FourDShape };
\ No newline at end of file
+export { FourDShape };
diff --git a/main.js b/main.js
index a3725e9..dc6c80f 100644
--- a/main.js
+++ b/main.js
@@ -8,6 +8,8 @@ import { FourDGUI } from './gui.js';
 import { FourDShape } from './fourDShape.js';
 import { get_colours } from './colours.js';
 
+const FACE_OPACITY = 0.3;
+
 // scene, lights and camera
 
 const scene = new THREE.Scene();
@@ -40,6 +42,17 @@ const node_ms = node_colours.map((c) => new THREE.MeshStandardMaterial({color: c
 
 const link_ms = [ material ];
 
+
+const face_ms = [
+	new THREE.MeshLambertMaterial( { color: 0x44ff44 } )
+	];
+
+for( const face_m of face_ms ) {
+	face_m.transparent = true;	
+	face_m.opacity = FACE_OPACITY;
+}
+
+
 const STRUCTURES = {
 	'5-cell': POLYTOPES.cell5(),
 	'16-cell': POLYTOPES.cell16(),
@@ -55,7 +68,8 @@ function createShape(name) {
 	if( shape ) {
 		scene.remove(shape);
 	}
-	shape = new FourDShape(node_ms, link_ms, STRUCTURES[name]);
+	console.log(STRUCTURES[name]);
+	shape = new FourDShape(node_ms, link_ms, face_ms, STRUCTURES[name]);
 	scene.add(shape);
 }
 
diff --git a/polytopes.js b/polytopes.js
index 2a86218..2f63dee 100644
--- a/polytopes.js
+++ b/polytopes.js
@@ -170,9 +170,82 @@ export const cell24 = () => {
 }
 
 
-// notes on coherent indexing
-// see table in https://en.wikipedia.org/wiki/120-cell - maybe adapt the
-// unit radius table
+// face detection for the 120-cell
+
+// NOTE: all of these return node ids, not nodes
+
+// return all the links which connect to a node
+
+function nodes_links(links, nodeid) {
+	return links.filter((l) => l.source === nodeid || l.target === nodeid);
+}
+
+// filter to remove a link to a given id from a set of links
+
+function not_to_this(link, nodeid) {
+	return !(link.source === nodeid || link.target === nodeid);
+}
+
+// given nodes n1, n2, return all neighbours of n2 which are not n1
+
+function unmutuals(links, n1id, n2id) {
+	const nlinks = nodes_links(links, n2id).filter((l) => not_to_this(l, n1id));
+	return nlinks.map((l) => {
+		if( l.source === n2id ) {
+			return l.target;
+		} else {
+			return l.source;
+		}
+	})
+}
+
+
+function fingerprint(ids) {
+	const sids = [...ids];
+	sids.sort();
+	return sids.join(',');
+}
+
+
+
+function auto_120cell_faces(links) {
+	const faces = [];
+	const seen = {};
+	let id = 1;
+	for( const edge of links ) {
+		const v1 = edge.source;
+		const v2 = edge.target;
+		const n1 = unmutuals(links, v2, v1);
+		const n2 = unmutuals(links, v1, v2);
+		const shared = [];
+		for( const a of n1 ) {
+			const an = unmutuals(links, v1, a);
+			for( const d of n2 ) {
+				const dn = unmutuals(links, v2, d);
+				for( const x of an ) {
+					for( const y of dn ) {
+						if( x == y ) {
+							shared.push([v1, a, x, d, v2])
+						}
+					}
+				}
+			}
+		}
+		if( shared.length !== 3 ) {
+			console.log(`Bad shared faces for ${edge.id} ${v1} ${v2}`);
+		}
+		for( const face of shared ) {
+			const fp = fingerprint(face);
+			if( !seen[fp] ) {
+				faces.push({ id: id, nodes: face });
+				id++;
+				seen[fp] = true;
+			}
+		}
+	}
+	return faces;
+}
+
 
 
 function make_120cell_vertices() {
@@ -310,8 +383,8 @@ export const cell120 = () => {
 		geometry: {
 			node_size: 0.02,
 			link_size: 0.02
-		}
-
+		},
+		faces: faces
 	}
 }