Uniform tessellation

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In mathematics, a uniform tessellation is a tessellation of a d-dimensional space, or a (hyper)surface, such that all its vertices are identical, i.e., there is the same combination and arrangement of faces at each vertex.

When applied to Euclidean space, the tessellation is most often assumed to be by polyhedra. Examples of 3D regular tessellations are those of layers of right prisms according to the three regular tessellations in 2D; that with square cuboids is in a way the most regular, especially with cubes, because then it is congruent in three independent directions.

When applied to surfaces, uniform tessellations are an important notion for Nonuniform rational B-splines (NURBS).

[edit] See also

• List of uniform tilings
• Convex uniform honeycomb
• Honeycomb (geometry)