The art of perfectly tiling a plane with shapes that fit together without gaps or overlaps, found everywhere from ancient mosaics to modern architecture.
A tessellation is a pattern of shapes that covers a surface completely without any gaps or overlaps. The word comes from the Latin tessella, meaning a small square tile used in Roman mosaics.
Tessellations appear throughout history and nature. From the intricate geometric tilework of Islamic architecture to the hexagonal cells of a honeycomb, these patterns demonstrate a deep mathematical harmony between shape and space.
Only three regular polygons can tessellate on their own: equilateral triangles, squares, and regular hexagons. However, when you combine shapes or use irregular forms, the possibilities become infinite.
From M.C. Escher's mind-bending lizards to the Alhambra's centuries-old tilework, tessellations have captivated artists, mathematicians, and architects alike.
Equilateral triangles are one of only three regular polygons that tessellate perfectly on their own.
The simplest tessellation, found in bathroom tiles, chessboards, and pixel grids worldwide.
Bees discovered it first: hexagons are the most efficient way to divide a surface into equal cells.
M.C. Escher transformed simple tessellations into interlocking birds, fish, and lizards.
Islamic artisans created extraordinarily complex tessellations using compass-and-straightedge geometry.
An aperiodic tessellation that never repeats, discovered by Roger Penrose in the 1970s.
Click the button to cycle through different tessellation types and see how shapes fit together.
Explore more pattern types that share connections with tessellations.