Escher tessellations are not true mathematical tessellations. A mathematical tessellation uses multiple copies of the sameshape (or a small number of shapes) to cover an infinite plane without gaps or overlaps.
Escher's art covers a finite area, not a plane. Also, his shapes are not exact copies but change gradually across the area covered. Some examples are:
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Maurits Cornelis Escher, more populaly known as MC Escher.
Maurits Cornelis Escher, better known as MC Escher.
An irregular tessellation is a tesselation made of irregular shapes. Escher is famous for drawing these with animals in them.
A tessellation or tiling of the plane is a collection of plane figures that fills the plane with no overlaps and no gaps. One may also speak of tessellations of the parts of the plane or of other surfaces. Generalizations to higher dimensions are also possible. Tessellations frequently appeared in the art of M.C. Escher. In Latin, tessella was a small cubical piece of clay, stone or glass used to make mosaics. The word "tessella" means "small square" (from "tessera", square, which in its turn is from the Greek word for "four"). It corresponds with the everyday term tiling which refers to applications of tessellation, often made of glazed clay. Tessellation in terms of tiling or mosaic means shapes - which can be regular, irregular, or representing a recognizable form - fitted together to form a pattern with no spaces between the shapes. The artist Maurice C Escher used tessellation a lot, quite brilliantly; you might like to look up his work on the internet.
Tessera can be any shape. Often they are assumed to be polygonal but that is not a requirement. To see tessellation based on other shapes see the set of "Symmetry" artwork by MC Escher.