This project is based heavily off AsherGlicks Charlie Cube. It uses a different construction method to achieve the same outcome. Instead of using additional supports the LED legs are used as the primary structure.
See the links for all the basic info on how the hardware and software works.
Arduino Pro Mini 5V
Or any other similar microcontroller
All instructions are identical to here with the following exception. Instead of using additional supports I have just used the LED legs for the primary structure on the "spires". I found this was much easier to put together than having to hold other pieces of metal in place.