Tesseractic tetracomb

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Tesseractic tetracomb
Perspective projection of a 3x3x3x3 red-blue chessboard.
Type	Regular tetracomb
Family	Hypercubic honeycomb
Schläfli symbols	{4,3,3,4} {4,3}x{4,3} {∞}x{∞}x{∞}x{∞} {4,3,31,1}
Coxeter-Dynkin diagrams
4-face type	{4,3,3}
Cell type	{4,3}
Face type	{4}
Edge figure	8 {4,3} (octahedron)
Vertex figure	16 {4,3,3} (16-cell)
Coxeter groups	[4,3,3,4] [4,3,31,1]
Dual	self-dual
Properties	vertex-transitive, edge-transitive, face-transitive, cell-transitive

The tesseractic tetracomb is the one of three regular space-filling tessellation (or honeycomb) in Euclidean 4-space. Four tesseracts meet at each face, and it is more explicitly called an order-4 tesseractic tetracomb.

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

[edit] See also

• Hypercubic honeycomb - The family of {4,3,...,3,4} tessellations.
• List of regular polytopes:
  • A list of the three regular tessellations of Euclidean 4-space
  • Penteract {4,3,3,3} - The regular 5-hypercube, which exists in 5-space with 3 tesseracts on each face. This could equivalently be considered an order-3 tesseractic tetracomb, on the 4-sphere.
  • Order-5 tesseractic tetracomb {4,3,3,5} - This higher tessellation can be constructed on a hyperbolic 4-space.

[edit] References

• Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 p.296, Table II: Regular honeycombs
• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)