This unlikely tangle is actually a fair 12 sided die. This is a much more interesting shape than the traditional regular dodecahedron.
This 12 sided die is a tetragonal pentagonal dodecahedron, an isohedron. Crystallographers know it as the tetartoid. It's a challenging shape to turn into a die since opposite faces aren't even close to being parallel. To make it work, I started from a wireframe of the shape then embedded parallel sides inside it. The result is one of the most unlikely looking dice I've seen.
For more information on unique dice shapes, see http://loki3.com/poly/fair-dice.html.
2.892 w x
2.892 d x
1.139 w x
1.139 d x