Icositetrachoronic tetracomb

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Icositetrachoronic tetracomb
A 24-cell and first layer of its adjacent 4-faces.
Type	Regular tetracomb
Schläfli symbol	{3,4,3,3}
Coxeter-Dynkin diagram
4-face type	{3,4,3}
Cell type	{3,4}
Face type	{3}
Edge figure	4 {3,3} (tetrahedron)
Vertex figure	8-cell
Coxeter group	[3,4,3,3]
Dual	{3,3,4,3}
Properties	vertex-transitive, edge-transitive, face-transitive, cell-transitive

The icositetrachoronic tetracomb is the one of three regular space-filling tessellation (or honeycomb) in Euclidean 4-space. The other two are the tesseractic tetracomb and the hexadecachoronic tetracomb.

Constructed from 24-cell facets, three per edge, it has no lower dimensional analogues.

There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored 24-cell facets. In all cases, 8 24-cells meet at each vertex, but the vertex figures have different symmetry generators.

Name	Coxeter group	Coxeter-Dynkin diagram	Facets (24-cells)	Vertex figure (8-cell)
Regular: Icositetrachoronic tetracomb	[3,4,3,3]		8:
Rectified hexadecachoronic tetracomb	[3,3,4,3]		6: 2:
Birectified tesseractic tetracomb	[4,3,3,4]		4,4:
Rectified alternated tesseractic tetracomb	[31,1,3,4]		2: 4: 2:
Rectified quartered tesseractic tetracomb	[31,1,1,1] or q[4,3,3,4]		2,2,2,2:

[edit] See also

• List of regular polytopes

[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)