diff --git a/gui.js b/gui.js
new file mode 100644
index 0000000..8396d88
--- /dev/null
+++ b/gui.js
@@ -0,0 +1,90 @@
+import { GUI } from 'lil-gui';
+
+
+const DEFAULT_SHAPE = '120-cell';
+const DEFAULT_COLOR = 0x90ebff;
+const DEFAULT_BG = 0xdddddd;
+
+
+
+
+// set up GUI
+
+const gui = new GUI();
+
+const linkUrl = new URL(window.location.toLocaleString());
+
+const link_params = {};
+
+const urlParams = linkUrl.searchParams;
+for( const param of [ "shape", "xRotate", "yRotate" ]) {
+	const value = urlParams.get(param);
+	if( value ) {
+		link_params[param] = value;
+	}
+}
+
+link_params['hyperplane'] = floatParam(urlParams, 'hyperplane');
+link_params['thickness'] = floatParam(urlParams, 'thickness');
+link_params['color'] = colorParam(urlParams, 'color', DEFAULT_COLOR);
+link_params['background'] = colorParam(urlParams, 'background', DEFAULT_BG);
+
+dpsi = floatParam(urlParams, 'dpsi');
+dtheta = floatParam(urlParams, 'dtheta');
+
+
+const gui_params = {
+	shape: link_params['shape'] || DEFAULT_SHAPE,
+	thickness: link_params['thickness'] || 1,
+	color: link_params['color'] || DEFAULT_COLOR,
+	background: link_params['background'] || DEFAULT_BG,
+	hyperplane: link_params['hyperplane'] || 2,
+	xRotate: link_params['xRotate'] || 'YW',
+	yRotate: link_params['yRotate'] || 'XZ',
+	damping: false,
+	"copy link": function () {
+		const url = new URL(linkUrl.origin + linkUrl.pathname);
+		url.searchParams.append("shape", gui_params.shape);
+		url.searchParams.append("thickness", gui_params.thickness.toString());
+		url.searchParams.append("color", hexToString(gui_params.color));
+		url.searchParams.append("background", hexToString(gui_params.background));
+		url.searchParams.append("hyperplane", gui_params.hyperplane.toString());
+		url.searchParams.append("xRotate", gui_params.xRotate);
+		url.searchParams.append("yRotate", gui_params.yRotate);
+		url.searchParams.append("dtheta", dtheta.toString());
+		url.searchParams.append("dpsi", dpsi.toString());
+		copyTextToClipboard(url);
+	}
+};
+
+
+
+gui.add(gui_params, 'shape',
+	[ '5-cell', '16-cell', 'tesseract', '24-cell', '120-cell', '600-cell' ]
+	).onChange(createShape)
+
+gui.add(gui_params, 'hyperplane', 1.5, 4);
+gui.add(gui_params, 'thickness', 0.01, 4);
+gui.addColor(gui_params, 'color').onChange((c) => {
+	console.log(`Setting material colour to ${c}`);
+	material.color = new THREE.Color(c);
+});
+gui.addColor(gui_params, 'background').onChange((c) => {
+	console.log(`Setting background colour to ${c}`);
+	scene.background = new THREE.Color(c);
+});
+gui.add(gui_params, 'xRotate', [ 'YW', 'YZ', 'ZW' ]);
+gui.add(gui_params, 'yRotate', [ 'XZ', 'XY', 'XW' ]);
+gui.add(gui_params, 'damping');
+gui.add(gui_params, 'copy link');
+
+const ROTFN = {
+	XY: rotXY,
+	XZ: rotXZ,
+	XW: rotXW,
+	YZ: rotYZ,
+	YW: rotYW,
+	ZW: rotZW,
+};
+
+
diff --git a/rotation.js b/rotation.js
new file mode 100644
index 0000000..27b3fc7
--- /dev/null
+++ b/rotation.js
@@ -0,0 +1,85 @@
+// hacky stuff for 4d rotations
+
+// see https://math.stackexchange.com/questions/1402362/can-rotations-in-4d-be-given-an-explicit-matrix-form#1402376
+
+import * as THREE from 'three';
+
+
+function rotZW(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		ctheta, -stheta, 0, 0,
+		stheta, ctheta, 0, 0,
+		0, 0, 1, 0,
+		0, 0, 0, 1
+		);
+}
+
+function rotYW(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		ctheta, 0, -stheta, 0,
+		0, 1, 0, 0,
+		stheta, 0, ctheta, 0,
+		0, 0, 0, 1,
+		);
+}
+
+function rotYZ(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		ctheta, 0, 0, -stheta,
+		0, 1, 0, 0,
+		0, 0, 1, 0,
+		stheta, 0, 0, ctheta, 
+		);
+}
+
+function rotXW(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		1, 0, 0, 0,
+		0, ctheta, -stheta, 0,
+		0, stheta, ctheta, 0,
+		0, 0, 0, 1
+		);
+}
+
+function rotXZ(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		1, 0, 0, 0,
+		0, ctheta, 0, -stheta,
+		0, 0, 1, 0,
+		0, stheta, 0, ctheta,
+		);
+}
+
+function rotXY(theta) {
+	const ctheta = Math.cos(theta);
+	const stheta = Math.sin(theta);
+	return new THREE.Matrix4(
+		1, 0, 0, 0,
+		0, 1, 0, 0,
+		0, 0, ctheta, -stheta,
+		0, 0, stheta, ctheta,
+		);
+}
+
+
+export const rotfn = {
+	XY: rotXY,
+	XZ: rotXZ,
+	XW: rotXW,
+	YZ: rotYZ,
+	YW: rotYW,
+	ZW: rotZW,
+};
+
+
+