Why do certain polygons not tessellate?

In the simplest case, let's suppose that we're considering regular polygons that all meet at their vertices. First, tile the plane with squares, and look at the point at which four squares meet. read more

Tessellations occur when a shape is repeated in an interlocking pattern that fully covers a flat surface, or plane, like the pieces of a puzzle. Some shapes cannot tessellate because they are not regular polygons or do not contain vertices (corner points). read more

In that case, some of them tessellate, and that case is worked out very well by Billy Woods. read more

The reason why some shapes cannot be tessellated is that they have one or more vertexes with angles that cannot be arranged with the angles of other tiles (including the 180 degree angle of a straight side), so as to total to 360 degrees. read more