The cubic honeycomb is the only regular tessellation (or honeycomb) in Euclidean 3-space. It is an analog of the square tiling of the plane. In mathematics, the Schläfli symbol is a simple notation that gives a summary of some important properties of a particular regular polytope. ... This page lists the regular polytopes in Euclidean space. ... A cube (or regular hexahedron) is a three-dimensional Platonic solid composed of six square faces, with three meeting at each vertex. ... A square as a geometric shape is described and illustrated at square (geometry). ... A square as a geometric shape is described and illustrated at square (geometry). ... An octahedron (plural: octahedra) is a polyhedron with eight faces. ... In algebraic topology, the Euler characteristic is a topological invariant (in fact, homotopy invariant) defined for a broad class of topological spaces. ... The symmetry group of an object (e. ... A tessellation of space fills space with solids, e. ... In geometry, the Square tiling is a regular tiling of the Euclidean plane. ...

Four cubes exist on each edge, and 8 cubes around each vertex. It is a self-dual tessellation.

It is related to the regular hypercube which exists in 4-space as a regular 4-polytope which has 3 cubes on an edge. In geometry, the tesseract, or hypercube, is a regular, convex polychoron with eight cubical cells. ...

It is one of 28 uniform tessellations of 3-space (called Andreini tessellations) using regular and semiregular polyhedral cells. The Andreini tessellations are tilings of three_dimensional space using Platonic and Archimedean solids such that all vertices are identical. ...