5-cubic honeycomb

In geometry, the 5-cubic honeycomb or penteractic honeycomb is the only regular space-filling tessellation (or honeycomb) in Euclidean 5-space. Four 5-cubes meet at each cubic cell, and it is more explicitly called an order-4 penteractic honeycomb.

5-cubic honeycomb
(no image)
Type	Regular 5-space honeycomb Uniform 5-honeycomb
Family	Hypercube honeycomb
Schläfli symbol	{4,33,4} t0,5{4,33,4} {4,3,3,31,1} {4,3,4}×{∞} {4,3,4}×{4,4} {4,3,4}×{∞}(2) {4,4}(2)×{∞} {∞}(5)
Coxeter-Dynkin diagrams
5-face type	{4,33} (5-cube)
4-face type	{4,3,3} (tesseract)
Cell type	{4,3} (cube)
Face type	{4} (square)
Face figure	{4,3} (octahedron)
Edge figure	8 {4,3,3} (16-cell)
Vertex figure	32 {4,33} (5-orthoplex)
Coxeter group	${\displaystyle {\tilde {C}}_{5}}$ [4,33,4]
Dual	self-dual
Properties	vertex-transitive, edge-transitive, face-transitive, cell-transitive

It is analogous to the square tiling of the plane and to the cubic honeycomb of 3-space, and the tesseractic honeycomb of 4-space.