If you have a VRML plugin you can see and investigate the complete polyhedron here. (You can check here and find available plugins for your browser/OS.) The polyhedron is a compound of 30 cubes and belongs to the symmetry group 30 | A5 x I / C2 x I / μ, as described in H.F.Verheyen's Symmetry Orbits. The angle μ uniquely identifies one compound in the group and may vary between 0 and 45 degrees (with 0 and 45 not included). For some angles μ the compound has some special properties. For this compound the angle μ = acos(√(5+√5)/√10) and for that angle the compound can be divided into six base elements: 5 | D20 x I / D4 x I, for which each order 20 symmetry axis shares an order 5 symmetry axis with the compound. (In the wrl model the base elements have different colours.) Also holds that each order 2 symmetry axis of the compound is shared by two order 2 symmetry axes of two base elements.
The model itself is built with 250 gr/m2 chromolux paper using the colour pearl. This colour was chosen, because the model was a wedding present for two friends of mine. I thought it was not fitting to use another colour and I am pretty satisfied with the result. Since the model is quite small for 30 cubes it was difficult to get all the edges straight, though I don't think that my friends will complain... ;)
Here are some more pictures of the model:
A complete table about cube compounds can be found here here.