Tessellations

The Ancient Greeks knew that there were just three regular tessellations of a plane: those formed by equilateral triangles, squares, and hexagons.

The Swiss mathematician Ludwig Schläfi showed that there are eight semiregular tessellations of a plane. See also the Islamic Tilings for a dazzling exploration of semiregular and related tilings, beautifully worked in ceramics.

The English mathematician Roger Penrose has devised some Aperiodic Tilings using a small set of regular tiles. These fill the plane but never repeat!

Incidentally, the name tessellation derives from the Greek Tessera, meaning 4, square, tile. Obviously, 4-square tiles are the easiest to make and fit together (and the way that your web browser tiles your screen!).



Regular : Square (2k)

Regular : Triangle (3k)

Regular : Hexagon (3k)

Semiregular : 3 Triangles, 2 Squares (35k)

Semiregular : 2 Triangles, Square, Triangle, Square (11k)

Semiregular : Triangle, Hexagon, Triangle, Hexagon (4k)

Semiregular : Triangle, Square, Hexagon, Square (8k)

Semiregular : Square, 2 Octagons (2k)

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