This is a projection into 3-space of the Gosset 421 polytope, which is itself a representation of the exceptional Lie group E8.
This group is connected to many areas of mathematics, and is regarded with awe by mathematicians for its pervasive presence and order.
E8 has recently received media attention as the centerpiece of A. Garrett Lisi's unified field theory, which if true would mean that it explains most aspects of the observable universe. Here's a handy model for pondering the possibility.
The mathematical data for this visualization was developed in Second Life by Wizard Gynoid, Desdemona Enfield and Nand Nerd, with guidance from Dr. Lisi. This projection is notable for showing all 240 vertices, arranged in the concentric circles that appear in the common 2D "spirograph" rendering of this polytope.
Laser etched glass