# Why do equilateral triangles tessellate?

Dec 14, 2015

A shape will tessellate if its vertices can have a sum of 360˚.

In an equilateral triangle, each vertex is 60˚. Thus, $6$ triangles can come together at every point because 6xx60˚=360˚.

This also explains why squares and hexagons tessellate, but other polygons like pentagons won't.

A square will form corners where $4$ squares meet, since 4xx90˚=360˚.

Similarly, a regular hexagon has an angle measure of 120˚, so $3$ regular hexagons will meet at a point in a hexagonal tessellation since 3xx120˚=360˚.

A pentagon, however, has an internal angle measure of 108˚, which isn't a nice factor of 360˚.