I started with a pattern from Eric Droug's excellent book Islamic Geometric Patterns, made some modifications using Flash and Illustrator, exported as a SVG, imported it into CorelDraw for use with NYC Resistor's lasercutter. Once the wood pieces were cut, I backed each piece with some translucent paper and glued it all together with Crazy glue. Final result can be seen here: flickr.com/photos/hirmes/3909380149/

Update: I forgot to mention that after the pieces came out of the lasercutter, the sides were beveled to 45 degrees on an edge sander so that the sides of the cube would match. (Thanks Bre!)