3D Hypocycloid Shape

var matrix:Matrix3D = new Matrix3D();
var verts:Vector.<Number> = new Vector.<Number>();
var pVerts:Vector.<Number> = new Vector.<Number>();
var uvts:Vector.<Number> = new Vector.<Number>();
const TWO_PI:Number=Math.PI * 2;
var step:Number=.05;

var brush:BitmapData = new BitmapData(3, 2, true, 0x41FFFFFF);
var n:Number=8;
var xp:Number=0,yp:Number=0,a:Number=12,t:Number=0;
for (var i:Number = 0; i<TWO_PI; i+=step) {
	for (var j:Number = 0; j<TWO_PI; j+=step) {
        // unoptimized for readability
	var cosi:Number = a/n * ((n - 1) * Math.cos(i) + Math.cos(Math.abs((n - 1) * i)));
	var sini:Number = a/n * ((n - 1) * Math.sin(i) - Math.sin(Math.abs((n - 1) * i)));
	var cosj:Number = a/n * ((n - 1) * Math.cos(j) + Math.cos(Math.abs((n - 1) * j)));
	var sinj:Number = a/n * ((n - 1) * Math.sin(j) - Math.sin(Math.abs((n - 1) * j)));
		verts.push(cosi * cosj);
		verts.push(sini * cosj);
		verts.push(a * sinj);
		pVerts.push(0),pVerts.push(0);
		uvts.push(0),uvts.push(0),uvts.push(0);
	}
}
var canvas:BitmapData=new BitmapData(400,400,false,0x000000);
addChild(new Bitmap(canvas));
var dx:Number=0;
var dy:Number=0;
addEventListener(Event.ENTER_FRAME, onLoop);
function onLoop(evt:Event):void {
	dx += (mouseX - dx)/4;
	dy += (mouseY - dy)/4;
	matrix.identity();
	matrix.appendRotation(dy,Vector3D.X_AXIS);
	matrix.appendRotation(dx,Vector3D.Y_AXIS);
	matrix.appendTranslation(200, 200, 0);
	Utils3D.projectVectors(matrix, verts, pVerts, uvts);
	canvas.lock();
	canvas.fillRect(canvas.rect, 0x000000);
	var p = new Point();
	for (var i:int = 0; i<pVerts.length; i+=2) {
		p.x = pVerts[i];
		p.y = pVerts[i + 1];
		canvas.copyPixels(brush, brush.rect, p, null, null, true);
	}
	canvas.unlock();
}

Taking the Hypocycloid stuff from yesterday into 3D…