This project is based heavily off AsherGlicks Charlie Cube. It uses a different construction method to achieve the same outcome.
Here is a demo video of the cube in action. I couldn't get the lighting right to make it any clearer. However I'm sure you get the idea. There are the following animations.
-Chase the dot
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.