Another Skew Polyhedron

thingiverse

This is the third and final polyhedron described by Coxeter in his 1937 paper - "Regular Skew Polyhedra in Three and Four Dimensions and their Topological Analogues", Proc. London Math. Soc. 43, ser 2, 33-62, 1937. The first two are modeled in thing:2884052 and thing:2899221. This polyhedron is composed of hexagons; the vertices of 6 hexagons meet at a point to form a 3 dimensional pattern. It is convenient to consider it as the four hexagonal faces of a truncated tetrahedron with the trigonal faces absent. Here are two models which illustrate how this pattern occurs. Six_hexagons.stl is composed of three truncated tetrahedra taken from the infinite array. It clearly shows a point where 6 hexagonal vertices meet. Eight_tts.stl is composed of 8 truncated tetrahedra chosen to be easily and quickly printed. Minimal models which illustrate the packing of the two earlier polyhedra have been added for comparison. They are six_squares.stl and four_hexagons.stl. OpenSCAD Code is included.