Euclidean tilings by convex regular polygons
Tilings of Regular Polygons
A [Regular_polygon|regular polygon] is a simple [polygon] made of equal lengths and equal angles.
Using regular polygons as "tiles" you can fill a flat surface with them.
What combination of polygons can fill a point is based on their internal angles. The internal angle of all polygons at a point must add to 360 degrees.
Interior angles:
- triangle - 60 degrees
- square - 90 degrees
- pentagon - 108 degrees
- hexagon - 120 degrees
Seeing these angles, you can immediately consider than:
- 6 triangles = 360 degrees
- 4 squares = 360 degrees
- 3 hexagons = 360 degrees
These, when repeated create the 3 "regular tessellations" in the plane