Demitesseractic tetracomb

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Demitesseractic tetracomb
Perspective projection: the first layer of adjacent 16-cell facets.
Type	Regular tetracomb
Family	Alternated hypercube honeycomb
Schläfli symbol	{3,3,4,3} h{4,3,3,4} {31,1,3,4} {31,1,1,1}
Coxeter-Dynkin diagram
4-face type	{3,3,4}
Cell type	{3,3}
Face type	{3}
Edge figure	cube
Vertex figure	24-cell
Coxeter group	[3,4,3,3] [4,3,31,1] [31,1,1,1]
Dual	{3,4,3,3}
Properties	vertex-transitive, edge-transitive, face-transitive, cell-transitive

The demitesseractic tetracomb or hexadecachoric 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 icositetrachoronic tetracomb. It is constructed from 16-cell polychoron facets, three around every edge. It has a 24-cell vertex figure.

As a regular honeycomb, {3,3,4,3}, it has no lower dimensional analogues, but as an alternated form, the (demitesseractic tetracomb), h{4,3,3,4}, it is related to the alternated cubic honeycomb.

It is also called a F4 lattice.

[edit] See also

• Cubic honeycomb
• Demipenteractic pentacomb
• List of regular polytopes

[edit] References

• Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8
  • pp. 154-156: Partial truncation or alternation, represented by h prefix: h{4,4}={4,4}; h{4,3,4}={3^1,1,4}, h{4,3,3,4}={3,3,4,3}, ...

• George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs)