The regular pentagon (with equal side lengths and equal angles between the sides) can not tile the plane, but some non-regular pentagons can. The hunt to classify the pentagons that can tile the plane has been a century-long mathematical quest begun by Karl Reinhardt in 1918 who discovered the first five types of pentagons that tile the plane. In 1968, R.B. Kershner found three more, then Richard James in 1975, and Marjorie Rice, Rolf Stein, and most recently University of Washington Bothell in August of 2015. Currently we are at 15 distinct classes of irregular pentagons that make it possible to tile the plane, covering it completely.

Pentagons are certainly the most intriguing polygon for tiling the plane, not only because of its odd number of sides but also because mathematicians thought they had exhausted the possibilities. Martin Gardner and Doris Schattschneider have mentioned and written about Penrose Tilings in various papers and books.
I have taken single sample tiles from mathematical papers and actually repeated them to cover a larger plane, displaying the different types of pentagonal classes in all their glory.

# PENTAGONAL TILING

- Author: Andrew Inhwan Kim
- Medium: Illustrator, Wacom Tablet
- Date: April 15, 2016
- Tags: Design, Patterns, Illustration, Math