Rectified 24cell honeycomb
In fourdimensional Euclidean geometry, the rectified 24cell honeycomb is a uniform spacefilling honeycomb. It is constructed by a rectification of the regular 24cell honeycomb, containing tesseract and rectified 24cell cells.
Rectified 24cell honeycomb  

(No image)  
Type  Uniform 4honeycomb 
Schläfli symbol  r{3,4,3,3} rr{3,3,4,3} r2r{4,3,3,4} r2r{4,3,3^{1,1}} 
CoxeterDynkin diagrams 

4face type  Tesseract Rectified 24cell 
Cell type  Cube Cuboctahedron 
Face type  Square Triangle 
Vertex figure  Tetrahedral prism 
Coxeter groups  , [3,4,3,3] , [4,3,3,4] , [4,3,3^{1,1}] , [3^{1,1,1,1}] 
Properties  Vertex transitive 
Alternate names
 Rectified icositetrachoric tetracomb
 Rectified icositetrachoric honeycomb
 Cantellated 16cell honeycomb
 Bicantellated tesseractic honeycomb
Symmetry constructions
There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored rectified 24cell and tesseract facets. The tetrahedral prism vertex figure contains 4 rectified 24cells capped by two opposite tesseracts.
Coxeter group  Coxeter diagram 
Facets  Vertex figure  Vertex figure symmetry (order) 

= [3,4,3,3] 
4: 1: 
(48)  
3: 1: 1: 
(12)  
= [4,3,3,4] 
2,2: 1: 
(8)  
= [3^{1,1},3,4] 
1,1: 2: 1: 
(4)  
= [3^{1,1,1,1}] 
1,1,1,1: 1: 
(2) 
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 93
 Klitzing, Richard. "4D Euclidean tesselations"., o3o3o4x3o, o4x3o3x4o  ricot  O93
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} 
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