12 Cubes Stuffed with Cube Symmetry
This is a model I am really proud of. I like this one a lot, because it is full of cube symmetry. For years and years I was trying to find somehting like this. Later I gave up and I thought another model would be the best approximation that exists. Finally I found that it was possible and enthousiastically I started developing the idea. However building this model took me a long time, not only because the model contains such tiny faces, but also because the summer of 2002 was incredibly beautiful in Sweden and I didn't want to spend too much time indoors.
The model belongs to the group 12B|S4xI|C2xI as described in H.F.Verheyen's Symmetry Orbits. This one appears for the angle μ=(1/2)atan((4/7)√2), but the angle isn't mentioned. In fact the special position isn't mentioned at all (which was the reason I gave up the idea for a while). This one is special, because it has a property that other compounds in that group do not have: it can be divided into 4 subcompounds of 3 cubes, which also have cube symmetry, i.e. it consists of 4 classic compounds of 3 cubes.
As I said, the model is stuffed with cube symmetry: it consists of 12 cubes, each sub-compound of one colour has cube symmetry, and the whole model has cube symmetry!