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.

Geometry

Manipulatives
Problem Posing
Problem Sets

MP1 - Make sense of problems and persevere in solving them.
MP3 - Construct viable arguments and critique others' reasoning.
MP5 - Use appropriate tools strategically.
MP6 - Attend to precision.
MP7 - Look for and make use of structure.
MP8 - Look for and express regularity in repeated reasoning.