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.
This model was heavily damaged in December 2018 when the closet that it was standing on suddenly fell when my youngest son went into his room. Luckily my son wasn't hurt. Only the floor and this model was broken. We got rid of the closet, it was a dangerously bad construction.
2012-05-30, 21:46