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In geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-transitive. Uniform tilings...

Weisstein, Eric W., "Dual polyhedron", MathWorld Weisstein, Eric W., "Dual tessellation", MathWorld Weisstein, Eric W., "Self-dual polyhedron", MathWorld...

each vertex. Its vertex figure is a regular octahedron. It is a self-dual tessellation with Schläfli symbol {4,3,4}. John Horton Conway called this honeycomb...

dual to that set's Delaunay triangulation. The Voronoi diagram is named after mathematician Georgy Voronoy, and is also called a Voronoi tessellation...

into pairs of dual polyhedra. Graph duality is a topological generalization of the geometric concepts of dual polyhedra and dual tessellations, and is in...

A tessellation or tiling is the covering of a surface, often a plane, using one or more geometric shapes, called tiles, with no overlaps and no gaps. In...

and catoptric tessellations as the uniform tessellations (or honeycombs) of Euclidean 3-space with prime space groups and their duals, as three-dimensional...

no gaps. It is an example of the more general mathematical tiling or tessellation in any number of dimensions. Its dimension can be clarified as n-honeycomb...

The Voronoi diagram of a regular triangular lattice is the honeycomb tessellation of hexagons. The maximal diameter (which corresponds to the long diagonal...

rank > 1 in higher dimensions. There are no Euclidean regular star tessellations in any number of dimensions. There is only one polytope of rank 1 (1-polytope)...

considered a tessellation. A regular polytope also has a dual polytope, represented by the Schläfli symbol elements in reverse order. A self-dual regular polytope...

In geometry, the square tiling, square tessellation or square grid is a regular tiling of the Euclidean plane. It has Schläfli symbol of {4,4}, meaning...

five solids into dual pairs. The tetrahedron is self-dual (i.e. its dual is another tetrahedron). The cube and the octahedron form a dual pair. The dodecahedron...

generalize the idea to include such objects as unbounded apeirotopes and tessellations, decompositions or tilings of curved manifolds including spherical polyhedra...

can be viewed as a disk as illustrated on the left. This image shows a tessellation of a disk by triangles and squares. One can define the distance between...

11-cell is not a tessellation of any manifold in the usual sense. Instead, the 11-cell is a locally projective polytope. It is self-dual and universal:...

In spherical geometry, an n-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite...

Euclidean tilings. The regular tiling {p,q} has a dual tiling {q,p} across the diagonal axis of the table. Self-dual tilings {2,2}, {3,3}, {4,4}, {5,5}, etc. pass...

segments, this tessellation is usually not considered to be an additional regular tessellation of the Euclidean plane, even when its dual order-2 apeirogonal...

3} is self-dual, {3, 4} is dual to {4, 3}, {4, 3, 3} to {3, 3, 4} and so on. The vertex figure of a regular polytope is the dual of the dual polytope's...