A defining featue of this non-convex 20 sided polyhedron is that all of its dihedral angles are 90 degrees including the concave angles (blue edges) as well as the convex angles (brown edges).
It is also a "shaky polyhedron" as explained at [mathworld](http://mathworld.wolfram.com/JessensOrthogonalIcosahedron.html) and [wikipedia](http://en.wikipedia.org/wiki/Jessen%27s_icosahedron).
This model was created with [vzome](http://www.vzome.com). The vzome model, a Collada DAE model and an OFF model are included in the zip download.