Skip to content # Tiling With Pentagons

## Activity Guide

# This guide looks at the activity in detail and goes into the underlying math.

Covington, Judith. (2022). Tiling With Pentagons. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/Tiling-With-Pentagons

Contributor(s): Judith Covington

Math Circles: MTC Network

- Activity Description
- Topics Covered
- Session Styles
- Mathematical Practices

A pentagonal tiling is a tiling of the plane where each individual piece is in the shape of a pentagon. The plane cannot be tiled with regular pentagons. However, are there any convex pentagons that can tile the plane? This session explores various pentagons and their tiling abilities.
From 1918 to 1985, fourteen irregular pentagons that would tile the plane were discovered. On August 14, 2015, Casey Mann, Jennifer McLoud, and David Von Derau of the University of Washington Bothell announced that they discovered a fifteenth pentagon. Interestingly, in 2017, Michaël Rao proved that there were no more than these fifteen