A shape is said to tessellate the plane if the plane can be covered without holes and no overlapping (save for the boundary points) with congruent copies of the shape.

Why do we need tessellations?

Such tilings may be decorative patterns, or may have functions such as providing durable and water-resistant pavement, floor or wall coverings. Historically, tessellations were used in Ancient Rome and in Islamic art such as in the Moroccan architecture and decorative geometric tiling of the Alhambra palace.

What does it mean to tessellate the plane?

A tessellation is created when a shape is repeated over and over again covering a plane without any gaps or overlaps. Another word for a tessellation is a tiling.