Models of a Skew Polyhedon

Models of a Skew Polyhedon

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This skew polyhedron was first described by Petrie in 1926 during a discussion with Coxeter. See Coxeter's paper "Regular Skew Polyhedra in Three and Four Dimensions and their Topological Analogues" Proc. London Math. Soc., ser 2, 43, 33-62, 1937. and also https://en.wikipedia.org/wiki/Regular_skew_apeirohedron It consists of a regular infinite array of squares, six of which surround each vertex. Here are models, similar to the one shown in Coxeter's paper, which illustrate this idea. OpenSCAD code is included. May 2, 2018. A simpler, more parametric version of the openSCAD code, "unit_cell_multiple.scad", was added. It was pointed out that this arrangement of squares is a member of space group 229 with 6 squares in the repeating unit - see the openSCAD code. "unit_cell_contents.stl", also added, shows the unit cell contents and clearly shows 6 squares meeting at a vertex.

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