I decided to study Archimedean solids for my press fit assembly kit because they are fairly simple to construct and offer interesting combinatorial and geometrical properties. All Archimedean solids (or semiregular polyhedra) are canonical polyhedras (in-sphere touching each all polyhedron's edges) and satisfy where rho is the sum of face-angles at a vertex and V denotes the number of vertices. Each of these solids have reciprocal polyhedras which are commonly called Catalan solids.

The Great Rhombicuboctahedron is a 26 faced Archimedean solid. It is composed out of 12 squares (12 {4}), 8 hexagrams (8 {6}) and 6 octagons (6{8}). Its vertices have the interesting property having Cartesian coordinates which are permutations of centered at the origin.

Tessellation of the of the Great Rhombicuboctahedron is represented above and is part of the 20 demiregular tessellations of the plane represented below.