Ideas in Geometry/Instructive examples/Lesson 15: Tessellations

2.3 Tessellations

A tessellation is a pattern of polygons fitted together to cover the entire plane without overlapping. A regular tessellation is a tessellation is when a regular polygon, a figure whose sides all have the same length and whose angles are all equal, tiles the plane.

The three regular polygons that can tile the plane are an equilateral triangle, a square, and a regular hexagon. This is possible because the interior angles of these three regular figures can be evenly go into 360 (the number of degrees in a circle).



Theorem: Any triangle and quadrilateral can tile the plane.