In geometry, an E9 honeycomb is a tessellation of uniform polytopes in hyperbolic 9-dimensional space.
, also (E10) is a paracompact hyperbolic group, so either facets or vertex figures will not be bounded.
E10 is last of the series of Coxeter groups with a bifurcated Coxeter-Dynkin diagram of lengths 6,2,1.
There are no regular honeycombs in the family since its Coxeter diagram is a nonlinear graph, but there are three simplest ones, with a single ring at the end of its 3 branches: 621, 261, 162.
The 621 honeycomb is constructed from alternating 9-simplex and 9-orthoplex facets within the symmetry of the E10 Coxeter group.
[1] It is created by a Wythoff construction upon a set of 10 hyperplane mirrors in 9-dimensional hyperbolic space.
The 621 is last in a dimensional series of semiregular polytopes and honeycombs, identified in 1900 by Thorold Gosset.
It is created by a Wythoff construction upon a set of 10 hyperplane mirrors in 9-dimensional hyperbolic space.
Removing the node on the end of the 6-length branch leaves the 251 honeycomb.
It is created by a Wythoff construction upon a set of 10 hyperplane mirrors in 9-dimensional space.