Pentagonal Tile (R3)

This is the fundamental design for a type 3 pentagonal tiling of the Euclidean plane. K. Reinhardt discovered five families of convex pentagons that could tile the plane in 1918. (1-5). Pentagons in Group 3 can be tiled in 3 by 3.

The tile's STL and Scad files are included, as well as an image of multiple tiles being tiled. The Type 3 Pentagram is also a member of the p3 wallpaper group, indicating that the pentagon has symmetry.

The group p3 contains three rotation centers of order three (120°), but no reflections or glide reflections. It has convex pentagons and one rotational order. b is customizable and modified the angles and sides for the pentagon based on the angles and sides elements.

This tile was created for George Mason University's MATH401: Mathematics Through 3D Printing course. This topic is taught by Evelyn Sander in the fall of 2021.