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# Demitesseractic honeycomb

Perspective projection: the first layer of adjacent 16-cell facets.
Type Regular 4-space honeycomb
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 honeycomb or hexadecachoric honeycomb is the one of three regular space-filling tessellation (or honeycomb) in Euclidean 4-space. The other two are the tesseractic honeycomb and the icositetrachoric honeycomb. 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 honeycomb), h{4,3,3,4}, it is related to the alternated cubic honeycomb.

It is also called a F4 lattice.

## 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} = {31,1,4}, 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)

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