Some shapes can be used to tessellate the plane, while other shapes cannot. For example, a square or an equilateral triangle can tessellate the plane (in fact any triangle or parallelogram can), but if you try to cover the plane with a regular pentagon, you'll find there's no way to do it without leaving gaps.

How do you know that an equilateral triangle will tessellate?

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 6×60˚=360˚ . This also explains why squares and hexagons tessellate, but other polygons like pentagons won't.

Can all triangles tessellate?

The simplest polygons have three sides, so we begin with triangles: All triangles tessellate. ... The sum of angles of any triangle is 180°. Moving up from triangles, we turn to four sided polygons, the quadrilaterals.