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This odd looking shape is actually a fair 12 sided die. Results are read from the top side of the shape embedded in the wireframe.
This 12 sided die has a convex hull that's a triakis tetrahedron, an isohedron. The triakis tetrahedron is a tricky shape to turn into a die since opposite sides aren't parallel. But by embedding a second triakis tetrahedron inside a wireframe, I was able to create parallel sides. The end result is a very distinctive 12 sided die.
For more information on unique dice shapes, see http://loki3.com/poly/fair-dice.html.