Runcicantitruncated 5-cell honeycomb

Runcicantitruncated 4-simplex honeycomb
(No image)
Type	Uniform 4-honeycomb
Schläfli symbol	t0,1,2,3{3[5]}
Coxeter–Dynkin diagram
4-face types	t0,1,3{33} t0,1,2{33} t0,1,2,3{33}
Cell types	Cuboctahedron Truncated octahedron Truncated tetrahedron Hexagonal prism Triangular prism
Vertex figure	tilted rectangular duopyramid
Symmetry	×2, [[3[5]]]
Properties	vertex-transitive

In four-dimensional Euclidean geometry, the runcicantitruncated 4-simplex honeycomb or runcicantitruncated 5-cell honeycomb is a space-filling tessellation honeycomb.

Alternate names

• Great cycloprismated pentachoric tetracomb
• Grand prismatodispentachoric tetracomb

Related polytopes and honeycombs

This honeycomb is one of seven unique uniform honeycombs^[1] constructed by the Coxeter group. The symmetry can be multiplied by the symmetry of rings in the Coxeter–Dynkin diagrams:

Pentagon symmetry	Extended symmetry	Extended diagram	Extended order	Honeycomb diagrams
a1	[3[5]]		×1	(None)
i2	[[3[5]]]		×2	1, 2, 3,  4, 5, 6
r10	[5[3[5]]]		×10	7

See also

Regular and uniform honeycombs in 4-space:

• tesseractic honeycomb
• 16-cell honeycomb
• 24-cell honeycomb
• Truncated 24-cell honeycomb
• Snub 24-cell honeycomb
• 5-cell honeycomb
• Truncated 5-cell honeycomb

Notes

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, Wiley-Interscience Publication, 1995, ISBN 978-0-471-01003-6
  • (Paper 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10] (1.9 Uniform space-fillings)
  • (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 139
• Richard Klitzing, 4D, Euclidean tesselations x3x3x3x3o3*a - gocypapit - O139

v t e Fundamental convex regular and uniform honeycombs in dimensions 2–11
Family					/ /
Uniform tiling	{3[3]}	δ3	hδ3	qδ3	Hexagonal
Uniform convex honeycomb	{3[4]}	δ4	hδ4	qδ4
Uniform 5-honeycomb	{3[5]}	δ5	hδ5	qδ5	24-cell honeycomb
Uniform 6-honeycomb	{3[6]}	δ6	hδ6	qδ6
Uniform 7-honeycomb	{3[7]}	δ7	hδ7	qδ7	222
Uniform 8-honeycomb	{3[8]}	δ8	hδ8	qδ8	133 • 331
Uniform 9-honeycomb	{3[9]}	δ9	hδ9	qδ9	152 • 251 • 521
Uniform n-honeycomb	{3[n]}	δn	hδn	qδn	1k2 • 2k1 • k21