A Second Infinite Skew Polyhedron

thingiverse

Here is the second polyhedron that Petrie presented to Coxeter in 1926, accessible at https://www.thingiverse.com/thing:2884052 - This polyhedron consists of hexagons. The vertices of four hexagons converge at a point; this pattern is repeated in three dimensions to form a skew polyhedron. Like the previous polyhedron, this pattern belongs to space group 229 with 4 hexagons as the repeating unit. It's more convenient to consider a unit cell containing eight hexagons arranged like a hollow truncated octahedron lacking square faces. The following three models illustrate how this pattern occurs.\r\n\r\nThe STL files t_octa_1.stl and t_octa_7.stl can be combined to form a group of 8 truncated octahedra. Removing t_octa_1.stl reveals the interior space, clearly showing how four hexagonal vertices meet. T_octa_27.stl is an expanded version of this pattern.\r\n\r\nOpenSCAD code is provided.