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Why do equilateral triangles tessellate?

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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. read more

Because two sets of equally spaced lines in two linearly independent directions will carve the plane into parallelograms. read more

Each angle in an equilateral triangle is 60 degrees. In order to create a regular tessellation of an area, we need for the angles of the polygons we are putting near each other to sum to 360 degrees. If you place six equilateral triangles so that all of them share a vertex, and each triangle is adjacent to two others, you get 60*6 = 360 degrees in that vertex. read more

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