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Runcinated 5-orthoplexes
From Wikipedia, the free encyclopedia
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In five-dimensional geometry, a runcinated 5-orthoplex is a convex uniform 5-polytope with 3rd order truncation (runcination) of the regular 5-orthoplex.
There are 8 runcinations of the 5-orthoplex with permutations of truncations, and cantellations. Four are more simply constructed relative to the 5-cube.
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Runcinated 5-orthoplex
Runcinated 5-orthoplex | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,3{3,3,3,4} | |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 162 | |
Cells | 1200 | |
Faces | 2160 | |
Edges | 1440 | |
Vertices | 320 | |
Vertex figure | ![]() | |
Coxeter group | B5 [4,3,3,3] D5 [32,1,1] | |
Properties | convex |
Alternate names
- Runcinated pentacross
- Small prismated triacontiditeron (Acronym: spat) (Jonathan Bowers)[1]
Coordinates
The vertices of the can be made in 5-space, as permutations and sign combinations of:
- (0,1,1,1,2)
Images
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Runcitruncated 5-orthoplex
Alternate names
- Runcitruncated pentacross
- Prismatotruncated triacontiditeron (Acronym: pattit) (Jonathan Bowers)[2]
Coordinates
Cartesian coordinates for the vertices of a runcitruncated 5-orthoplex, centered at the origin, are all 80 vertices are sign (4) and coordinate (20) permutations of
- (±3,±2,±1,±1,0)
Images
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Runcicantellated 5-orthoplex
Runcicantellated 5-orthoplex | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,2,3{3,3,3,4} t0,2,3{3,3,31,1} | |
Coxeter-Dynkin diagram | ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 162 | |
Cells | 1200 | |
Faces | 2960 | |
Edges | 2880 | |
Vertices | 960 | |
Vertex figure | ![]() | |
Coxeter group | B5 [4,3,3,3] D5 [32,1,1] | |
Properties | convex |
Alternate names
- Runcicantellated pentacross
- Prismatorhombated triacontiditeron (Acronym: pirt) (Jonathan Bowers)[3]
Coordinates
The vertices of the runcicantellated 5-orthoplex can be made in 5-space, as permutations and sign combinations of:
- (0,1,2,2,3)
Images
Runcicantitruncated 5-orthoplex
Summarize
Perspective
Runcicantitruncated 5-orthoplex | ||
Type | Uniform 5-polytope | |
Schläfli symbol | t0,1,2,3{3,3,3,4} | |
Coxeter-Dynkin diagram |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
4-faces | 162 | |
Cells | 1440 | |
Faces | 4160 | |
Edges | 4800 | |
Vertices | 1920 | |
Vertex figure | ![]() Irregular 5-cell | |
Coxeter groups | B5 [4,3,3,3] D5 [32,1,1] | |
Properties | convex, isogonal |
Alternate names
- Runcicantitruncated pentacross
- Great prismated triacontiditeron (gippit) (Jonathan Bowers)[4]
Coordinates
The Cartesian coordinates of the vertices of a runcicantitruncated 5-orthoplex having an edge length of √2 are given by all permutations of coordinates and sign of:
Images
Snub 5-demicube
The snub 5-demicube defined as an alternation of the omnitruncated 5-demicube is not uniform, but it can be given Coxeter diagram or
and symmetry [32,1,1]+ or [4,(3,3,3)+], and constructed from 10 snub 24-cells, 32 snub 5-cells, 40 snub tetrahedral antiprisms, 80 2-3 duoantiprisms, and 960 irregular 5-cells filling the gaps at the deleted vertices.
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Related polytopes
This polytope is one of 31 uniform 5-polytopes generated from the regular 5-cube or 5-orthoplex.
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Notes
References
External links
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