The Pentagonal Tiling Type 13

The Pentagonal Tiling Type 13
Heegyung Kim
September 10, 2021
George Mason University MATH 401: Mathematics Through 3D Printing

A pentagonal tiling is a process of covering a plane or space with geometric shapes of the pentagon. It cannot be overlap nor have gaps between the shapes. Including the recent discovery by Mann/McLoud/Von Derau in 2015, there are 15 types of pentagonal tiling. Eight of them are edge-to-edge (types 1, 2, 4, 5, 6, 7, 8, and 9) and seven of them are non-edge-to-edge (types 3, 10, 11, 12, 13, 14, and 15).

This 3D-printed object represents a pentagonal tiling of type 13. It is discovered by Marjorie Rice in 1977. This is a 2-isohedral and contains an 8-tile primitive unit. For type 13, the side d=2a=2e and the angle B=E=90° and angle 2A+D=360°. For this object, the dimensions are 40 x 40 x 4.5 in mm.

I used OpenSCad to build this object and exported it as an STL file. Then, for printing, two 3D printers were used: Ultimaker Cura and MakerBot Replicatio