diff --git a/fourDShape.js b/fourDShape.js
index c4b61dc..00040d8 100644
--- a/fourDShape.js
+++ b/fourDShape.js
@@ -7,15 +7,6 @@ const NODE_SIZE = 0.08;
 const LINK_SIZE = 0.02;
 
 
-function fourDtoV3(x, y, z, w, rotations) {
-	const v4 = new THREE.Vector4(x, y, z, w);
-	for ( const m4 of rotations ) {
-		v4.applyMatrix4(m4);
-	}
-	const k = HYPERPLANE / (HYPERPLANE + v4.w);
-	return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
-}
-
 
 class FourDShape extends THREE.Group {
 
@@ -26,9 +17,12 @@ class FourDShape extends THREE.Group {
 		this.nodes4 = structure.nodes;
 		this.nodes3 = {};
 		this.links = structure.links;
+		this.hyperplane = HYPERPLANE;
 		this.initShapes();
 	}
 
+
+
 	// if a node/link has no label, use the 0th material
 
 	getMaterial(entity, materials) {
@@ -77,9 +71,19 @@ class FourDShape extends THREE.Group {
 		link.object.children[0].rotation.x = Math.PI / 2.0;
 	}
 
+	fourDtoV3(x, y, z, w, rotations) {
+		const v4 = new THREE.Vector4(x, y, z, w);
+		for ( const m4 of rotations ) {
+			v4.applyMatrix4(m4);
+		}
+		const k = this.hyperplane / (this.hyperplane + v4.w);
+		return new THREE.Vector3(v4.x * k, v4.y * k, v4.z * k);
+	}
+
+
 	initShapes() {
 		for( const n of this.nodes4 ) {
-			const v3 = fourDtoV3(n.x, n.y, n.z, n.w, []);
+			const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, []);
 			const material = this.getMaterial(n, this.node_ms);
 			this.nodes3[n.id] = {
 				v3: v3,
@@ -92,9 +96,10 @@ class FourDShape extends THREE.Group {
 		}
 	}
 
+
 	render3(rotations) {
 		for( const n of this.nodes4 ) {
-			const v3 = fourDtoV3(n.x, n.y, n.z, n.w, rotations);
+			const v3 = this.fourDtoV3(n.x, n.y, n.z, n.w, rotations);
 			this.nodes3[n.id].v3 = v3;
 			this.nodes3[n.id].object.position.copy(v3);
 			// could do scaling here
diff --git a/main.js b/main.js
index 2df7bbe..873137c 100644
--- a/main.js
+++ b/main.js
@@ -4,6 +4,7 @@ import * as POLYTOPES from './polytopes.js';
 
 import { FourDShape } from './fourDShape.js';
 
+import { GUI } from 'lil-gui';
 
 
 
@@ -149,12 +150,29 @@ for( const link_m of link_ms ) {
 	}
 }
 
-const struct = POLYTOPES.cell24();
+const STRUCTURES = {
+	'5-cell': POLYTOPES.cell5(),
+	'16-cell': POLYTOPES.cell16(),
+	'tesseract': POLYTOPES.tesseract(),
+	'24-cell': POLYTOPES.cell24(),
+};
+
+let shape = false;
+
+function createShape(name) {
+	if( shape ) {
+		scene.remove(shape);
+	}
+
+	shape = new FourDShape(node_ms, link_ms, STRUCTURES[name]);
+	scene.add(shape);
+
+}
 
 
-const shape = new FourDShape(node_ms, link_ms, struct);
 
-scene.add(shape);
+
+createShape('24-cell');
 
 
 camera.position.z = 4;
@@ -185,6 +203,34 @@ renderer.domElement.addEventListener("mousemove", (event) => {
 	}
 })
 
+// set up GUI
+
+const gui = new GUI();
+
+const gui_params = {
+	shape: '24-cell',
+	hyperplane: 2,
+	xRotate: 'YW',
+	yRotate: 'XZ',
+};
+
+gui.add(gui_params, 'shape',
+	[ '5-cell', '16-cell', 'tesseract', '24-cell' ]
+	).onChange(createShape)
+
+gui.add(gui_params, 'hyperplane', 1, 4);
+gui.add(gui_params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
+gui.add(gui_params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
+
+const ROTFN = {
+	XY: rotXY,
+	XZ: rotXZ,
+	XW: rotXW,
+	YZ: rotYZ,
+	YW: rotYW,
+	ZW: rotZW,
+};
+
 
 
 const rotation = new THREE.Matrix4();
@@ -192,7 +238,11 @@ const rotation = new THREE.Matrix4();
 function animate() {
 	requestAnimationFrame( animate );
 
-	const rotations = [rotYZ(theta), rotXZ(psi)];
+	const rotations = [
+		ROTFN[gui_params.xRotate](theta), 
+		ROTFN[gui_params.yRotate](psi)
+	];
+	shape.hyperplane = gui_params.hyperplane;
 	shape.render3(rotations);
 
 	renderer.render( scene, camera );
diff --git a/package-lock.json b/package-lock.json
index 8a313b4..643cdbd 100644
--- a/package-lock.json
+++ b/package-lock.json
@@ -5,6 +5,7 @@
   "packages": {
     "": {
       "dependencies": {
+        "lil-gui": "^0.18.2",
         "three": "^0.154.0"
       },
       "devDependencies": {
@@ -414,6 +415,11 @@
         "node": "^8.16.0 || ^10.6.0 || >=11.0.0"
       }
     },
+    "node_modules/lil-gui": {
+      "version": "0.18.2",
+      "resolved": "https://registry.npmjs.org/lil-gui/-/lil-gui-0.18.2.tgz",
+      "integrity": "sha512-DgdrLy3/KGC0PiQLKgOcJMPItP4xY4iWgJ9+91Zaxfr8GCTmMps05QS9w9jW7yspILlbscbquwjOwxmWnSx5Uw=="
+    },
     "node_modules/nanoid": {
       "version": "3.3.6",
       "resolved": "https://registry.npmjs.org/nanoid/-/nanoid-3.3.6.tgz",
diff --git a/package.json b/package.json
index dc3017c..5bb9681 100644
--- a/package.json
+++ b/package.json
@@ -1,5 +1,6 @@
 {
   "dependencies": {
+    "lil-gui": "^0.18.2",
     "three": "^0.154.0"
   },
   "devDependencies": {