Convex regular icosahedrons contain 30 edges and 12 vertices. This makes for an interesting math problem, but as demonstrated by this project out of the LVL1 hackerspace in Louisville, Kentucky, its geometry also presents an excellent target for a massive number of LEDs.

Their build, in fact, consists of 708 programmable LEDs arranged facing inward on the edges and doubled over on each vertex support. These supports lead to a central stainless steel ball, reflecting a massive amount of light to the surrounding area. 

Everything is controlled by an Arduino Mega, along with an Uno-style prototyping shield, and power is provided by a massive 5V 60A supply unit.