Uniform coloring

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Uniform tiling 63-t0.png
111
Uniform tiling 63-t12.png
112
Uniform tiling 333-t012.png
123
The hexagonal tiling has 3 uniform colorings.
The square tiling has 9 uniform colorings:
1111, 1112(a), 1112(b),
1122, 1123(a), 1123(b),
1212, 1213, 1234.

In geometry, a uniform coloring is a property of a uniform figure (uniform tiling or uniform polyhedron) that is colored to be vertex-transitive. Different symmetries can be expressed on the same geometric figure with the faces following different uniform color patterns.

A uniform coloring can be specified by listing the different colors with indices around a vertex figure.

n-uniform figures[edit]

In addition, an n-uniform coloring is a property of a uniform figure which has n types vertex figure, that are collectively vertex transitive.

References[edit]

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