A Second Infinite Skew Polyhedron

thingiverse

Here is the second polyhedron that Petrie presented to Coxeter in 1926. see - https://www.thingiverse.com/thing:2884052 - This polyhedron is composed of hexagons. The vertices of four hexagons meet at a point; the pattern is repeated in three dimensions to make a skew polyhedron. Like the previous polyhedron this pattern is a member of space group 229 with 4 hexagons as the repeating unit. However it is convenient to consider a unit cell containing eight hexagons arranged like a hollow truncated octahedron lacking square faces. Here are 3 models which illustrate how this pattern occurs. t_octa_1.stl and t_octa_7.stl fit together to form a group of 8 truncated octahedra. t_octa_1.stl can be removed to reveal the interior space and clearly show the way in which 4 hexagonal vertices meet. t_octa_27.stl is an expanded version of the pattern. OpenSCAD code is included.