I derived this model from a Trapezoidal Icositetrahedron, which consists of 24 kites. It is a beautiful variant of the dual of a Rhombicuboctahedron. The variant is described here.

It can be derived from this variant by using the fact that both this variant and the Rhombic Dodecahedron have a ring of six faces that are parallel to an 3-fold axis.

I am not sure when I derived and built this model, but I guess it must have been around 1998. Most of the calculations were done by hand, but if I remember well I started using an algebraic system towards the end. The pieces were drawn by hand using a ruler and pencil and cut out by scissors.

The model belongs to the symmetry group of the Tetrahedron multiplied by the central inversion, indicated by Coxeter as A4 x {I}. I built this one to derive a compound of twelve cubes that consists of four classic compounds of three cubes. Later on I found that there are many of them. Never mind this one has the special relationship with the Trapezoidal Icositretrahedron.

2012-05-30, 21:46