Bitruncated 24-cell honeycomb

Bituncated 24-cell honeycomb
(No image)
Type Uniform 4-honeycomb
Schläfli symbol 2t{3,4,3,3}
Coxeter-Dynkin diagrams

4-face type t{4,3,3}
2t{3,4,3}
Cell type t{4,3}
{3,3}
Face type {3}, {8}
Vertex figure
Coxeter groups , [3,4,3,3]
Properties Vertex transitive

In four-dimensional Euclidean geometry, the bitruncated 24-cell honeycomb is a uniform space-filling honeycomb. It can be seen as a bitruncation of the regular 24-cell honeycomb, constructed by truncated tesseract and bitruncated 24-cell cells.

Alternate names edit

  • Bitruncated icositetrachoric tetracomb/honeycomb
  • Small tetracontaoctachoric tetracomb (baticot)

Related honeycombs edit

The [3,4,3,3],          , Coxeter group generates 31 permutations of uniform tessellations, 28 are unique in this family and ten are shared in the [4,3,3,4] and [4,3,31,1] families. The alternation (13) is also repeated in other families.

F4 honeycombs
Extended
symmetry
Extended
diagram
Order Honeycombs
[3,3,4,3]           ×1

          1,           3,           5,           6,           8,
          9,           10,           11,           12

[3,4,3,3]           ×1

          2,           4,           7,           13,
          14,           15,           16,           17,
          18,           19,           20,           21,
          22          23,           24,           25,
          26,           27,           28,           29

[(3,3)[3,3,4,3*]]
=[(3,3)[31,1,1,1]]
=[3,4,3,3]
       
=     
=          
×4

          (2),           (4),           (7),           (13)

See also edit

Regular and uniform honeycombs in 4-space:

References edit

  • Coxeter, H.S.M. Regular Polytopes, (3rd edition, 1973), Dover edition, ISBN 0-486-61480-8 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, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6 [1]
    • (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
  • George Olshevsky, Uniform Panoploid Tetracombs, Manuscript (2006) (Complete list of 11 convex uniform tilings, 28 convex uniform honeycombs, and 143 convex uniform tetracombs) Model 113
  • Klitzing, Richard. "4D Euclidean tesselations". o3o3x4x3o - baticot - O113

o3o3x4o3x - sricot - O112

Space Family           /   /  
E2 Uniform tiling {3[3]} δ3 3 3 Hexagonal
E3 Uniform convex honeycomb {3[4]} δ4 4 4
E4 Uniform 4-honeycomb {3[5]} δ5 5 5 24-cell honeycomb
E5 Uniform 5-honeycomb {3[6]} δ6 6 6
E6 Uniform 6-honeycomb {3[7]} δ7 7 7 222
E7 Uniform 7-honeycomb {3[8]} δ8 8 8 133331
E8 Uniform 8-honeycomb {3[9]} δ9 9 9 152251521
E9 Uniform 9-honeycomb {3[10]} δ10 10 10
E10 Uniform 10-honeycomb {3[11]} δ11 11 11
En-1 Uniform (n-1)-honeycomb {3[n]} δn n n 1k22k1k21