Truncated 24cell honeycomb
In fourdimensional Euclidean geometry, the truncated 24cell honeycomb is a uniform spacefilling honeycomb. It can be seen as a truncation of the regular 24cell honeycomb, containing tesseract and truncated 24cell cells.
Truncated 24cell honeycomb  

(No image)  
Type  Uniform 4honeycomb 
Schläfli symbol  t{3,4,3,3} tr{3,3,4,3} t2r{4,3,3,4} t2r{4,3,3^{1,1}} t{3^{1,1,1,1}} 
CoxeterDynkin diagrams 

4face type  Tesseract Truncated 24cell 
Cell type  Cube Truncated octahedron 
Face type  Square Triangle 
Vertex figure  Tetrahedral pyramid 
Coxeter groups  , [3,4,3,3] , [4,3,3^{1,1}] , [4,3,3,4] , [3^{1,1,1,1}] 
Properties  Vertex transitive 
It has a uniform alternation, called the snub 24cell honeycomb. It is a snub from the construction. This truncated 24cell has Schläfli symbol t{3^{1,1,1,1}}, and its snub is represented as s{3^{1,1,1,1}}.
Alternate names
 Truncated icositetrachoric tetracomb
 Truncated icositetrachoric honeycomb
 Cantitruncated 16cell honeycomb
 Bicantitruncated tesseractic honeycomb
Symmetry constructions
There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored truncated 24cell facets. In all cases, four truncated 24cells, and one tesseract meet at each vertex, but the vertex figures have different symmetry generators.
Coxeter group  Coxeter diagram 
Facets  Vertex figure  Vertex figure symmetry (order) 

= [3,4,3,3] 
4: 1: 
(24)  
= [3,3,4,3] 
3: 1: 1: 
(6)  
= [4,3,3,4] 
2,2: 1: 
(4)  
= [3^{1,1},3,4] 
1,1: 2: 1: 
(2)  
= [3^{1,1,1,1}] 
1,1,1,1: 1: 
[ ]^{+} (1) 
See also
Regular and uniform honeycombs in 4space:
References
 Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0486614808 p. 296, Table II: Regular honeycombs
 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 24) H.S.M. Coxeter, Regular and SemiRegular Polytopes III, [Math. Zeit. 200 (1988) 345]
 George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 99
 Klitzing, Richard. "4D Euclidean tesselations". o4x3x3x4o, x3x3x *b3x4o, x3x3x *b3x *b3x, o3o3o4x3x, x3x3x4o3o  ticot  O99
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} 