Question

Why do equilateral triangles tessellate?

Answer 1

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˚`.