diff --git a/fourDShape.js b/fourDShape.js
index 888ebd7..3ccc923 100644
--- a/fourDShape.js
+++ b/fourDShape.js
@@ -1,9 +1,12 @@
 import * as THREE from 'three';
 
+import { TaperedLink } from './taperedLink.js';
+
 
 const HYPERPLANE = 2.0;
 const W_FORESHORTENING = 0.04;
 
+
 class FourDShape extends THREE.Group {
 
 	constructor(node_ms, link_ms, face_ms, structure) {
@@ -42,7 +45,7 @@ class FourDShape extends THREE.Group {
 		return sphere;
 	}
 
-	makeLink(material, link) {
+	makeLink(basematerial, link) {
 		const n1 = this.nodes3[link.source];
 		const n2 = this.nodes3[link.target];
 		const s1 = n1.scale;
@@ -50,17 +53,11 @@ class FourDShape extends THREE.Group {
 		const length = n1.v3.distanceTo(n2.v3);
 		const centre = new THREE.Vector3();
 		centre.lerpVectors(n1.v3, n2.v3, 0.5);
-		const geometry = new THREE.CylinderGeometry(
-			this.link_scale * s2, this.link_scale * s1, 1,
-			16, 1, true
-		);
-		const cyl = new THREE.Mesh(geometry, material);
-		const edge = new THREE.Group();
-		edge.add(cyl);
+
+		const edge = new TaperedLink(basematerial);
+		edge.update(s1, s2, length);
 		edge.position.copy(centre);
-		edge.scale.copy(new THREE.Vector3(1, 1, length));
 		edge.lookAt(n2.v3);
-		cyl.rotation.x = Math.PI / 2.0;
 		this.add(edge);
 		return edge;
 	}
@@ -73,14 +70,9 @@ class FourDShape extends THREE.Group {
 		const length = n1.v3.distanceTo(n2.v3);
 		const centre = new THREE.Vector3();
 		centre.lerpVectors(n1.v3, n2.v3, 0.5);
-		// take the average of the ends as the thickness - as a workaround,
-		// because I haven't worked out how to reshape tapered links without
-		// having to reassign a new geometry to every link
-		const link_mean = this.link_scale * (s1 + s2) * 0.5;		
-		link.object.scale.copy(new THREE.Vector3(link_mean, link_mean, length));
-		link.object.position.copy(centre);
+		link.object.update(s1, s2, length);
+		link.object.position.copy(n1.v3);
 		link.object.lookAt(n2.v3);
-		link.object.children[0].rotation.x = Math.PI / 2.0;
 		link.object.visible = (!links_show || link.label in links_show); 
 	}
 
diff --git a/gui.js b/gui.js
index baba2ea..57df9d4 100644
--- a/gui.js
+++ b/gui.js
@@ -7,7 +7,7 @@ const DEFAULTS = {
 	linksize: 0.2,
 	linkopacity: 0.75,
 	link2opacity: 0.75,
-	shape: '120-cell',
+	shape: '16-cell',
 	option: 'none',
 	visibility: 5,
 	inscribed: false,
diff --git a/main.js b/main.js
index 04d8497..b285ae2 100644
--- a/main.js
+++ b/main.js
@@ -31,6 +31,10 @@ camera.lookAt(0, 0, 0);
 
 const renderer = new THREE.WebGLRenderer({antialias: true});
 renderer.setSize( window.innerWidth, window.innerHeight );
+
+renderer.localClippingEnabled = true;
+
+
 document.body.appendChild( renderer.domElement );
 
 // set up colours and materials for gui callbacks
diff --git a/taperedLink.js b/taperedLink.js
new file mode 100644
index 0000000..0ccfcf7
--- /dev/null
+++ b/taperedLink.js
@@ -0,0 +1,36 @@
+import * as THREE from 'three';
+
+
+class TaperedLink extends THREE.Group {
+
+  constructor(baseMaterial) {
+    super();
+    const geometry = new THREE.ConeGeometry( 0.75, 1, 32, true );
+    const cplane = new THREE.Plane(new THREE.Vector3(0, -1, 0), 0.5);
+    const material = baseMaterial.clone();
+    material.clippingPlanes = [ cplane ];
+    this.object = new THREE.Mesh( geometry, material );
+    this.add( this.object );
+  }  
+
+  update(r1, r2, l) {
+    const kraw = ( r1 - r2 );
+    const k = ( kraw == 0 ) ? 0.001 : kraw;
+    if( k > 0 ) {
+      const h = l * r1 / k;
+      this.object.scale.copy(new THREE.Vector3(r1, h, r1));
+      this.object.material.clippingPlanes[0].normal.y = -1;
+      this.object.material.clippingPlanes[0].constant = l / 2;
+      this.object.position.copy(new THREE.Vector3(0, h/2 - l/2, 0));
+    } else {
+      const h = l * r2 / k;
+      this.object.scale.copy(new THREE.Vector3(r2, h, r2));
+      this.object.material.clippingPlanes[0].normal.y = 1;
+      this.object.material.clippingPlanes[0].constant = l / 2;
+      this.object.position.copy(new THREE.Vector3(0, h / 2 + l / 2, 0));
+    }
+  }
+
+}
+
+export { TaperedLink };