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In
geometryGeometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....
, a
uniform coloring is a property of a uniform figure (
uniform tilingIn geometry, a uniform tiling is a tessellation of the plane by regular polygon faces with the restriction of being vertex-uniform.Uniform tilings can exist in both the Euclidean plane and hyperbolic plane...
or
uniform polyhedronA uniform polyhedron is a polyhedron which has regular polygons as faces and is vertex-transitive...
) that is colored to be
vertex-transitiveIn geometry, a polytope is isogonal or vertex-transitive if, loosely speaking, all its vertices are the same...
. Different
symmetriesSymmetry generally conveys two primary meanings. The first is an imprecise sense of harmonious or aesthetically pleasing proportionality and balance; such that it reflects beauty or perfection...
can be expressed on the same geometric figure with the
facesIn geometry, a face of a polyhedron is any of the polygons that make up its boundaries. For example, any of the squares that bound a cube is a face of the cube...
following different uniform color patterns.
A
uniform coloring can be specified by listing the different colors by indices around a
vertex figureIn geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
.
n-uniform figures
In addition, an
n-uniform coloring is a property of a
uniform figure which has
n types
vertex figureIn geometry a vertex figure is, broadly speaking, the figure exposed when a corner of a polyhedron or polytope is sliced off.-Definitions - theme and variations:...
, that are collectively vertex transitive.
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