Cyclotruncated 8simplex honeycomb
In eightdimensional Euclidean geometry, the cyclotruncated 8simplex honeycomb is a spacefilling tessellation (or honeycomb). The tessellation fills space by 8simplex, truncated 8simplex, bitruncated 8simplex, tritruncated 8simplex, and quadritruncated 8simplex facets. These facet types occur in proportions of 2:2:2:2:1 respectively in the whole honeycomb.
Cyclotruncated 8simplex honeycomb  

(No image)  
Type  Uniform honeycomb 
Family  Cyclotruncated simplectic honeycomb 
Schläfli symbol  t_{0,1}{3^{[9]}} 
Coxeter diagram  
8face types  {3^{7}} t_{1,2}{3^{7}} t_{3,4}{3^{7}} 
Vertex figure  Elongated 7simplex antiprism 
Symmetry  ×2, [[3^{[9]}]] 
Properties  vertextransitive 
Structure
It can be constructed by nine sets of parallel hyperplanes that divide space. The hyperplane intersections generate cyclotruncated 7simplex honeycomb divisions on each hyperplane.
Related polytopes and honeycombs
This honeycomb is one of 45 unique uniform honeycombs[1] constructed by the Coxeter group. The symmetry can be multiplied by the ring symmetry of the Coxeter diagrams:
A8 honeycombs  

Enneagon symmetry 
Symmetry  Extended diagram 
Extended group 
Honeycombs 
a1  [3^{[9]}] 
 
i2  [[3^{[9]}]]  ×2 
 
i6  [3[3^{[9]}]]  ×6  
r18  [9[3^{[9]}]]  ×18 
See also
Regular and uniform honeycombs in 8space:
Notes

 Weisstein, Eric W. "Necklace". MathWorld., OEIS sequence A000029 461 cases, skipping one with zero marks
References
 Norman Johnson Uniform Polytopes, Manuscript (1991)
 Kaleidoscopes: Selected Writings of H.S.M. Coxeter, edited by F. Arthur Sherk, Peter McMullen, Anthony C. Thompson, Asia Ivic Weiss, WileyInterscience Publication, 1995, ISBN 9780471010036
 (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380407, MR 2,10] (1.9 Uniform spacefillings)
 (Paper 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345]
Fundamental convex regular and uniform honeycombs in dimensions 29  

Space  Family  / /  
E^{2}  Uniform tiling  {3^{[3]}}  δ_{3}  hδ_{3}  qδ_{3}  Hexagonal 
E^{3}  Uniform convex honeycomb  {3^{[4]}}  δ_{4}  hδ_{4}  qδ_{4}  
E^{4}  Uniform 4honeycomb  {3^{[5]}}  δ_{5}  hδ_{5}  qδ_{5}  24cell honeycomb 
E^{5}  Uniform 5honeycomb  {3^{[6]}}  δ_{6}  hδ_{6}  qδ_{6}  
E^{6}  Uniform 6honeycomb  {3^{[7]}}  δ_{7}  hδ_{7}  qδ_{7}  2_{22} 
E^{7}  Uniform 7honeycomb  {3^{[8]}}  δ_{8}  hδ_{8}  qδ_{8}  1_{33} • 3_{31} 
E^{8}  Uniform 8honeycomb  {3^{[9]}}  δ_{9}  hδ_{9}  qδ_{9}  1_{52} • 2_{51} • 5_{21} 
E^{9}  Uniform 9honeycomb  {3^{[10]}}  δ_{10}  hδ_{10}  qδ_{10}  
E^{n1}  Uniform (n1)honeycomb  {3^{[n]}}  δ_{n}  hδ_{n}  qδ_{n}  1_{k2} • 2_{k1} • k_{21} 