Skip to content # Semiregular Tilings

## Activity Guide

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

Bennett, Hannah. White, Nina. (2022). Semiregular Tilings. In S. Bowen (Ed.), Math Circle Activity Database. American Institute of Mathematics. https://mathcircles.org/activity/semiregular-tilings

Contributor(s): Hanna Bennett, Nina White

Math Circles: MTC Network

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

Can you find all possible semiregular tilings of the plane? A tiling of the plane covers the (infinite) plane, without gaps or overlaps, using congruent copies of one or more shapes. A semiregular tiling is a tiling of the plane with certain constraints: two or more regular polygons are used, polygons meet edge-to-edge, and the pattern of polygons around every vertex is the same.
Questions about polygonal tilings of the plane can utilize a classical area of mathematics to highlight and connect middle and high school mathematics content standards, mathematical practices, and the nuanced nature of mathematical justification. This session considers special categories of tilings and asks what possibilities exist under these constraints.