Cubic Honeycomb

The cubic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 3-space, made up of cubic cells. It has 4 cubes around every edge, and 8 cubes around each vertex. Its vertex figure is a regular octahedron.

It is a self-dual tessellation with Schläfli symbol {4,3,4}. It is part of a multidimensional family of hypercube honeycombs, with Schläfli symbols of the form {4,3,...,3,4}, starting with the square tiling, {4,4} in the plane.

It is one of 28 uniform honeycombs using convex uniform polyhedral cells.

Read more about Cubic Honeycomb:  Uniform Colorings, Related Polytopes and Tesellations

Other articles related to "honeycomb, cubic honeycomb, honeycombs, cubic":

Tetrahedral-octahedral Honeycomb
... The tetrahedral-octahedral honeycomb or alternated cubic honeycomb is a space-filling tessellation (or honeycomb) in Euclidean 3-space ... tessellations called alternated hypercubic honeycombs, formed as an alternation of a hypercubic honeycomb and being composed of demihypercube and cross-polytope facets ... In this case of 3-space, the cubic honeycomb is alternated, reducing the cubic cells to tetrahedra, and the deleted vertices create octahedral voids ...
Tetrahedral-octahedral Honeycomb - Symmetry - Projection By Folding
... The alternated cubic honeycomb can be orthogonally projected into the planar square tiling by a geometric folding operation that maps one pairs of mirrors into each other ... The projection of the alternated cubic honeycomb creates two offset copies of the square tiling vertex arrangement of the plane Coxeter group Coxeter diagram Graph alternated cubic ...
Simplicial Polytope - Examples
... regular 4-polytope 4-simplex, 16-cell, 600-cell Dual convex uniform honeycombs Disphenoid tetrahedral honeycomb Dual of cantitruncated cubic honeycomb Dual of omnitruncated cubic honeycomb ...
Cubes - Related Polyhedra - In Uniform Honeycombs and Polychora
... It is an element of 9 of 28 convex uniform honeycombs Cubic honeycomb Truncated square prismatic honeycomb Snub square prismatic honeycomb Elongated triangular prismatic honeycomb Gyroelongated ...
Cubic Honeycomb - Related Polytopes and Tesellations
... The expanded cubic honeycomb is geometrically identical to the cubic honeycomb , ] , It is related to the regular 4-polytope tesseract, Schläfli symbol {4,3 ... It's also related to the order-5 cubic honeycomb, Schläfli symbol {4,3,5}, of hyperbolic space with 5 cubes around each edge ...

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