For several years I had been walking around with the idea for this model, when I finally had enough time to develope it. With help of an algebraic system it took me something like 3 months to calculate the things I needed, and to write the documentation. Building took me 5 months...I should say 4 months, because I had a break of one month when I was half way.

The whole model is a compound of 12 cubes with four colours. The model belongs to the symmetry group of the tetrahedron multiplied by the central inversion, indicated by Coxeter as A4 x {I}. Each colour forms a compound of 3 cubes. These compounds are the Classic Compounds of 3 cubes and belong to the same symmetry group as the cube itself.

Another special property is that you'll get a Trapezoidal Icositretrahedron, which is the dual of a Rhombicubocatahedron, if you take one sort of pairs of parallel squares.