Rectified 24-cell honeycomb

Rectified 24-cell honeycomb
(No image)
TypeUniform 4-honeycomb
Schläfli symbolr{3,4,3,3}
rr{3,3,4,3}
r2r{4,3,3,4}
r2r{4,3,31,1}
Coxeter-Dynkin diagrams




=
=
=

4-face typeTesseract
Rectified 24-cell
Cell typeCube
Cuboctahedron
Face typeSquare
Triangle
Vertex figure
Tetrahedral prism
Coxeter groups{\tilde{F}}_4, [3,4,3,3]
{\tilde{C}}_4, [4,3,3,4]
{\tilde{B}}_4, [4,3,31,1]
{\tilde{D}}_4, [31,1,1,1]
PropertiesVertex transitive

In four-dimensional Euclidean geometry, the rectified 24-cell honeycomb is a uniform space-filling honeycomb. It is constructed by a rectification of the regular 24-cell honeycomb, containing tesseract and rectified 24-cell cells.

Alternate names

Symmetry constructions

There are five different symmetry constructions of this tessellation. Each symmetry can be represented by different arrangements of colored rectified 24-cell and tesseract facets. The tetrahedral prism vertex figure contains 4 rectified 24-cells capped by two opposite tesseracts.

Coxeter group Coxeter
diagram		 Facets Vertex figure Vertex
figure
symmetry
(order)
{\tilde{F}}_4
= [3,4,3,3]		 4:
1: 		, [3,3,2]
(48)
3:
1:
1: 		, [3,2]
(12)
{\tilde{C}}_4
= [4,3,3,4]		 2,2:
1: 		, [2,2]
(8)
{\tilde{B}}_4
= [31,1,3,4]		 1,1:
2:
1: 		, [2]
(4)
{\tilde{D}}_4
= [31,1,1,1]		 1,1,1,1:

1: 		, []
(2)

See also

Regular and uniform honeycombs in 4-space:

References

Fundamental convex regular and uniform honeycombs in dimensions 2–10
Family {\tilde{A}}_{n-1} {\tilde{C}}_{n-1} {\tilde{B}}_{n-1} {\tilde{D}}_{n-1} {\tilde{G}}_2 / {\tilde{F}}_4 / {\tilde{E}}_{n-1}
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
This article is issued from Wikipedia - version of the Friday, September 18, 2015. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.