Penteractic pentacomb

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Penteractic pentacomb
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Type	Regular pentacomb
Family	Hypercube honeycomb
Schläfli symbol	{4,3,3,3,4} {4,3,4} x {∞} {4,4} x {∞} x {∞} {∞} x {∞} x {∞} x {∞} {4,4} x {4,4}
Coxeter-Dynkin diagrams
5-face type	{4,3,3,3}
4-face type	{4,3,3}
Cell type	{4,3}
Face type	{4}
Face figure	{4,3} (octahedron)
Edge figure	8 {4,3,3} (16-cell)
Vertex figure	32 {4,3,3,3} (pentacross)
Coxeter group	[4,3,3,3,4]
Dual	self-dual
Properties	vertex-transitive, edge-transitive, face-transitive, cell-transitive

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

It is an analog of the square tiling of the plane, the cubic honeycomb of 3-space, and the tesseractic tetracomb of 4-space.

It is also related to the regular hexeract which exists in 6-space with 3 penteracts on each cell. This could be considered as a tessellation on the 5-sphere, an order-3 penteractic pentacomb, {4,3,3,3,3}.