Stericantitruncated 16-cell honeycomb

Stericantitruncated 16-cell honeycomb
(No image)
Type Uniform 4-honeycomb
Schläfli symbol t0,1,2,4{3,3,4,3}
s2,3,4{3,4,3,3}
Coxeter-Dynkin diagrams
4-face type

t0,1,2{3,3,4}
t0,1,3{4,3,3}
t0,1,2{4,3}x{}
t1{4,3}x{} {3}x{6}

Cell type
Face type
Vertex figure
Coxeter groups , [3,4,3,3]
Properties Vertex transitive

In four-dimensional Euclidean geometry, the stericantitruncated 16-cell honeycomb is a uniform space-filling honeycomb.

Alternate names

edit
  • Great cellirhombated icositetrachoric tetracomb (gicaricot)
  • Runcicantic hexadecachoric tetracomb
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 121 (Wrongly named runcinated icositetrachoric honeycomb)
  • Klitzing, Richard. "4D Euclidean tesselations". x3x3x4o3x - gicaricot - O130
Space Family           /   /  
E2 Uniform tiling 0[3] δ3 3 3 Hexagonal
E3 Uniform convex honeycomb 0[4] δ4 4 4
E4 Uniform 4-honeycomb 0[5] δ5 5 5 24-cell honeycomb
E5 Uniform 5-honeycomb 0[6] δ6 6 6
E6 Uniform 6-honeycomb 0[7] δ7 7 7 222
E7 Uniform 7-honeycomb 0[8] δ8 8 8 133331
E8 Uniform 8-honeycomb 0[9] δ9 9 9 152251521
E9 Uniform 9-honeycomb 0[10] δ10 10 10
E10 Uniform 10-honeycomb 0[11] δ11 11 11
En-1 Uniform (n-1)-honeycomb 0[n] δn n n 1k22k1k21