Google Classroom
GeoGebraGeoGebra Classroom

Introduction

Definition: A shape P tessellates if it is possible to fill the entire plane with rotations and or translations of P with no overlapping area. Three regular polygons tesselate the Euclidean plane. Which ones? Adjust "Sides" and "Copies" to explore.
What are the three regular polygons that tessellate the plane? If p = the number of sides of the polygon and q = the minimum number of copies at a vertex, list all pairs (p,q) that tessellate the plane. Why does the regular pentagon not tessellate the plane? Why are there no tessellations by regular polygons with 7 or more sides?