Tessellation

A tessellation is a pattern of shapes that fit together perfectly to cover a plane with no gaps or overlaps. From the Latin tessella (small tile), tessellations appear everywhere in nature and design: honeycomb cells, dragon scales, cracked mud, and the eyes of insects all demonstrate this principle of efficient space-filling.

The simplest tessellations use regular polygons—only three shapes tessellate the plane alone: equilateral triangles, squares, and regular hexagons. However, combining multiple shapes opens infinite possibilities. Symmetry governs which patterns work, making tessellation a bridge between mathematics, spatial design, and art.

Medieval Islamic artisans mastered complex tessellations in tile work centuries before mathematicians formalized them. The Dutch artist M.C. Escher made tessellation famous by filling tessellating grids with interlocking creatures and impossible objects—showing that mathematical constraints can paradoxically liberate creativity.

Tessellations extend beyond 2D: vectors and crystal structures create three-dimensional tessellations, while abstract tessellations explore hyperbolic and spherical geometries. Today they're essential in computer graphics, architectural design, and materials science.

Related

Polygon, Symmetry, M.C. Escher, Sacred geometry, Tiling, Crystal structure