Is It A Tessellation Or Not?

Defining tessellation through examples
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According to M. C. Escher, a tessellation is "a regular division of a plane".

On this website, we define a tessellation as "a repetitive interlocking pattern of shapes. The pattern fills, or clearly could fill, a surface entirely without gaps or overlaps". A tessellation looks a bit like a simple jigsaw puzzle, but all the pieces are just one or two or three shapes. We also prefer that the shapes' silhouettes resemble some other object: cat, camera, catfish, catapult, cabbage...anything that has a definite, recognizable shape.

Occasionally, a tessellation fills a 2D surface that isn't an infinitely wide plane. For example, that surface might be the outside of a ball, the outside of a lampshade, the inside of a decorated egg, the skin of a snake, a flat hexagon, a big wall, or a "circle limit". Also, occasionally a tessellation fills a surface that isn't flat, like the outside of a soccer ball or a dodecahedron.

On this page, you'll find examples of art. Some of the artwork is by children, some by adults, and some even by the past and present webmasters of You should judge for yourself whether each artwork is a tessellation, and then you'll have the chance to compare your decision with the webmaster's opinion.

You may also enjoy the free lesson plan "Geometry in Computer Games? An Exploration of Tessellations Used in neXtu", which includes a free downloadable PowerPoint presentation, "Am I a Tessellation?" which invites the audience to create a definition of tessellation by critiquing several examples. That lesson plan was created in February of 2014 by the National Council of Teachers of Mathematics (NCTM).