Some shapes do not tessellate because overlaps and gaps within the plane are not allowed. If a shape tessellates, then its corners are able to meet at one single point. In addition, some of the shapes tessellate simply because there are certain points at which multiple vertices intersect.
A tessellation of a flat surface is the tiling of a plane using one or more geometric shapes, called tiles, with no overlaps and no gaps. In mathematics, tessellations can be...