A tiling of regular polygons (in two dimensions), polyhedra (three dimensions),
or polytopes ( dimensions) is called a tessellation. Tessellations can be
specified using a Schläfli symbol .
The breaking up of self-intersecting polygons into simple polygons is also called tessellation (Woo
et al. 1999), or more properly, polygon
tessellation .
There are exactly three regular tessellations
composed of regular polygons symmetrically tiling the plane.
Tessellations of the plane by two or more convex regular polygons such that the same polygons in the same order surround
each polygon vertex are called semiregular
tessellations , or sometimes Archimedean tessellations. In the plane, there are
eight such tessellations, illustrated above (Ghyka 1977, pp. 76-78; Williams
1979, pp. 37-41; Steinhaus 1999, pp. 78-82; Wells 1991, pp. 226-227).
There are 14 demiregular (or polymorph) tessellations which are orderly compositions of the three regular and eight semiregular
tessellations (Critchlow 1970, pp. 62-67; Ghyka 1977, pp. 78-80; Williams
1979, p. 43; Steinhaus 1999, pp. 79 and 81-82).
In three dimensions, a polyhedron which is capable of tessellating space is called a space-filling
polyhedron . Examples include the cube , rhombic
dodecahedron , and truncated octahedron .
There is also a 16-sided space-filler and a convex polyhedron
known as the Schmitt-Conway biprism which
fills space only aperiodically.
A tessellation of -dimensional
polytopes is called a honeycomb .
See also Archimedean Solid ,
Cairo Tessellation ,
Cell ,
Demiregular
Tessellation ,
Dual Tessellation ,
Hexagonal
Grid ,
Hinged Tessellation ,
Honeycomb ,
Honeycomb Conjecture ,
Kepler's
Monsters ,
Regular Tessellation ,
Schläfli
Symbol ,
Semiregular Polyhedron ,
Semiregular Tessellation ,
Space-Filling
Polyhedron ,
Spiral Similarity ,
Square
Grid ,
Symmetry ,
Tiling ,
Triangular Grid ,
Triangular
Symmetry Group ,
Triangulation ,
Wallpaper
Groups
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Cite this as:
Weisstein, Eric W. "Tessellation." From
MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/Tessellation.html
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