Truncated 8-simplexes

Orthogonal projections in A₈ Coxeter plane
File:8-simplex t0.svg 8-simplex File:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png	File:8-simplex t01.svg Truncated 8-simplex File:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png	File:8-simplex t1.svg Rectified 8-simplex File:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png
File:8-simplex t34.svg Quadritruncated 8-simplex File:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png	File:8-simplex t23.svg Tritruncated 8-simplex File:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png	File:8-simplex t12.svg Bitruncated 8-simplex File:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png

In eight-dimensional geometry, a truncated 8-simplex is a convex uniform 8-polytope, being a truncation of the regular 8-simplex. There are four unique degrees of truncation. Vertices of the truncation 8-simplex are located as pairs on the edge of the 8-simplex. Vertices of the bitruncated 8-simplex are located on the triangular faces of the 8-simplex. Vertices of the tritruncated 8-simplex are located inside the tetrahedral cells of the 8-simplex.

Truncated 8-simplex

Truncated 8-simplex
Type	uniform 8-polytope
Schläfli symbol	t{3⁷}
Coxeter-Dynkin diagrams	File:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges	288
Vertices	72
Vertex figure	( )v{3,3,3,3,3}
Coxeter group	A₈, [3⁷], order 362880
Properties	convex

Alternate names

Truncated enneazetton (Acronym: tene) (Jonathan Bowers)^[1]

Coordinates

The Cartesian coordinates of the vertices of the truncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,0,1,2). This construction is based on facets of the truncated 9-orthoplex.

Images

orthographic projections
A_k Coxeter plane	A₈	A₇	A₆	A₅
Graph	File:8-simplex t01.svg	File:8-simplex t01 A7.svg	File:8-simplex t01 A6.svg	File:8-simplex t01 A5.svg
Dihedral symmetry	[9]	[8]	[7]	[6]
A_k Coxeter plane	A₄	A₃	A₂
Graph	File:8-simplex t01 A4.svg	File:8-simplex t01 A3.svg	File:8-simplex t01 A2.svg
Dihedral symmetry	[5]	[4]	[3]

Bitruncated 8-simplex

Bitruncated 8-simplex
Type	uniform 8-polytope
Schläfli symbol	2t{3⁷}
Coxeter-Dynkin diagrams	File:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges	1008
Vertices	252
Vertex figure	{ }v{3,3,3,3}
Coxeter group	A₈, [3⁷], order 362880
Properties	convex

Alternate names

Bitruncated enneazetton (Acronym: batene) (Jonathan Bowers)^[2]

Coordinates

The Cartesian coordinates of the vertices of the bitruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,0,1,2,2). This construction is based on facets of the bitruncated 9-orthoplex.

Images

orthographic projections
A_k Coxeter plane	A₈	A₇	A₆	A₅
Graph	File:8-simplex t12.svg	File:8-simplex t12 A7.svg	File:8-simplex t12 A6.svg	File:8-simplex t12 A5.svg
Dihedral symmetry	[9]	[8]	[7]	[6]
A_k Coxeter plane	A₄	A₃	A₂
Graph	File:8-simplex t12 A4.svg	File:8-simplex t12 A3.svg	File:8-simplex t12 A2.svg
Dihedral symmetry	[5]	[4]	[3]

Tritruncated 8-simplex

tritruncated 8-simplex
Type	uniform 8-polytope
Schläfli symbol	3t{3⁷}
Coxeter-Dynkin diagrams	File:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges	2016
Vertices	504
Vertex figure	{3}v{3,3,3}
Coxeter group	A₈, [3⁷], order 362880
Properties	convex

Alternate names

Tritruncated enneazetton (Acronym: tatene) (Jonathan Bowers)^[3]

Coordinates

The Cartesian coordinates of the vertices of the tritruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,0,1,2,2,2). This construction is based on facets of the tritruncated 9-orthoplex.

Images

orthographic projections
A_k Coxeter plane	A₈	A₇	A₆	A₅
Graph	File:8-simplex t23.svg	File:8-simplex t23 A7.svg	File:8-simplex t23 A6.svg	File:8-simplex t23 A5.svg
Dihedral symmetry	[9]	[8]	[7]	[6]
A_k Coxeter plane	A₄	A₃	A₂
Graph	File:8-simplex t23 A4.svg	File:8-simplex t23 A3.svg	File:8-simplex t23 A2.svg
Dihedral symmetry	[5]	[4]	[3]

Quadritruncated 8-simplex

Quadritruncated 8-simplex
Type	uniform 8-polytope
Schläfli symbol	4t{3⁷}
Coxeter-Dynkin diagrams	File:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 3.pngFile:CDel node.png or File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.png
6-faces	18 3t{3,3,3,3,3,3}
7-faces
5-faces
4-faces
Cells
Faces
Edges	2520
Vertices	630
Vertex figure	File:Quadritruncated 8-simplex verf.png {3,3}v{3,3}
Coxeter group	A₈, [[3⁷]], order 725760
Properties	convex, isotopic

The quadritruncated 8-simplex an isotopic polytope, constructed from 18 tritruncated 7-simplex facets.

Alternate names

Octadecazetton (18-facetted 8-polytope) (Acronym: be) (Jonathan Bowers)^[4]

Coordinates

The Cartesian coordinates of the vertices of the quadritruncated 8-simplex can be most simply positioned in 9-space as permutations of (0,0,0,0,1,2,2,2,2). This construction is based on facets of the quadritruncated 9-orthoplex.

Images

orthographic projections
A_k Coxeter plane	A₈	A₇	A₆	A₅
Graph	File:8-simplex t34.svg	File:8-simplex t34 A7.svg	File:8-simplex t34 A6.svg	File:8-simplex t34 A5.svg
Dihedral symmetry	[[9]] = [18]	[8]	[[7]] = [14]	[6]
A_k Coxeter plane	A₄	A₃	A₂
Graph	File:8-simplex t34 A4.svg	File:8-simplex t34 A3.svg	File:8-simplex t34 A2.svg
Dihedral symmetry	[[5]] = [10]	[4]	[[3]] = [6]

Related polytopes

Isotopic uniform truncated simplices
Dim.	2	3	4	5	6	7	8
Name Coxeter	Hexagon File:CDel branch 11.png = File:CDel node 1.pngFile:CDel 6.pngFile:CDel node.png t{3} = {6}	Octahedron File:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.png = File:CDel node 1.pngFile:CDel 3.pngFile:CDel node.pngFile:CDel 4.pngFile:CDel node.png r{3,3} = {3^1,1} = {3,4} ${\begin{cases} 3 \\ 3 \end{cases}}$	Decachoron File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.png 2t{3³}	Dodecateron File:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.png 2r{3⁴} = {3^2,2} ${\begin{cases} 3, 3 \\ 3, 3 \end{cases}}$	Tetradecapeton File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.png 3t{3⁵}	Hexadecaexon File:CDel node 1.pngFile:CDel split1.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.png 3r{3⁶} = {3^3,3} ${\begin{cases} 3, 3, 3 \\ 3, 3, 3 \end{cases}}$	Octadecazetton File:CDel branch 11.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.png 4t{3⁷}
Images	File:Truncated triangle.svg	File:3-cube t2.svgFile:Uniform polyhedron-33-t1.svg	File:4-simplex t12.svgFile:Schlegel half-solid bitruncated 5-cell.png	File:5-simplex t2.svgFile:5-simplex t2 A4.svg	File:6-simplex t23.svgFile:6-simplex t23 A5.svg	File:7-simplex t3.svgFile:7-simplex t3 A5.svg	File:8-simplex t34.svgFile:8-simplex t34 A7.svg
Vertex figure	( )∨( )	File:Octahedron vertfig.svg { }×{ }	File:Bitruncated 5-cell verf.png { }∨{ }	File:Birectified hexateron verf.png {3}×{3}	File:Tritruncated 6-simplex verf.png {3}∨{3}	{3,3}×{3,3}	File:Quadritruncated 8-simplex verf.png {3,3}∨{3,3}
Facets		{3} File:Regular polygon 3 annotated.svg	t{3,3} File:Uniform polyhedron-33-t01.png	r{3,3,3} File:Schlegel half-solid rectified 5-cell.png	2t{3,3,3,3} File:5-simplex t12.svg	2r{3,3,3,3,3} File:6-simplex t2.svg	3t{3,3,3,3,3,3} File:7-simplex t23.svg
As intersecting dual simplexes	File:Regular hexagon as intersection of two triangles.png File:CDel branch 10.png ∩ File:CDel branch 01.png	File:Stellated octahedron A4 A5 skew.png File:CDel node.pngFile:CDel split1.pngFile:CDel nodes 10lu.png ∩ File:CDel node.pngFile:CDel split1.pngFile:CDel nodes 01ld.png	File:Compound dual 5-cells and bitruncated 5-cell intersection A4 coxeter plane.png File:CDel branch.pngFile:CDel 3ab.pngFile:CDel nodes 10l.png ∩ File:CDel branch.pngFile:CDel 3ab.pngFile:CDel nodes 01l.png	File:Dual 5-simplex intersection graph a5.pngFile:Dual 5-simplex intersection graph a4.png File:CDel node.pngFile:CDel split1.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes 10l.png ∩ File:CDel node.pngFile:CDel split1.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes 01l.png	File:CDel branch.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes 10l.png ∩ File:CDel branch.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes 01l.png	File:CDel node.pngFile:CDel split1.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes 10l.png ∩ File:CDel node.pngFile:CDel split1.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes 01l.png	File:CDel branch.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes 10l.png ∩ File:CDel branch.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes.pngFile:CDel 3ab.pngFile:CDel nodes 01l.png

Related polytopes

This polytope is one of 135 uniform 8-polytopes with A₈ symmetry.

A8 polytopes
File:8-simplex t0.svg t₀	File:8-simplex t1.svg t₁	File:8-simplex t2.svg t₂	File:8-simplex t3.svg t₃	File:8-simplex t01.svg t₀₁	File:8-simplex t02.svg t₀₂	File:8-simplex t12.svg t₁₂	File:8-simplex t03.svg t₀₃	File:8-simplex t13.svg t₁₃	File:8-simplex t23.svg t₂₃	File:8-simplex t04.svg t₀₄	File:8-simplex t14.svg t₁₄	File:8-simplex t24.svg t₂₄	File:8-simplex t34.svg t₃₄	File:8-simplex t05.svg t₀₅
File:8-simplex t15.svg t₁₅	File:8-simplex t25.svg t₂₅	File:8-simplex t06.svg t₀₆	File:8-simplex t16.svg t₁₆	File:8-simplex t07.svg t₀₇	File:8-simplex t012.svg t₀₁₂	File:8-simplex t013.svg t₀₁₃	File:8-simplex t023.svg t₀₂₃	File:8-simplex t123.svg t₁₂₃	File:8-simplex t014.svg t₀₁₄	File:8-simplex t024.svg t₀₂₄	File:8-simplex t124.svg t₁₂₄	File:8-simplex t034.svg t₀₃₄	File:8-simplex t134.svg t₁₃₄	File:8-simplex t234.svg t₂₃₄
File:8-simplex t015.svg t₀₁₅	File:8-simplex t025.svg t₀₂₅	File:8-simplex t125.svg t₁₂₅	File:8-simplex t035.svg t₀₃₅	File:8-simplex t135.svg t₁₃₅	File:8-simplex t235.svg t₂₃₅	File:8-simplex t045.svg t₀₄₅	File:8-simplex t145.svg t₁₄₅	File:8-simplex t016.svg t₀₁₆	File:8-simplex t026.svg t₀₂₆	File:8-simplex t126.svg t₁₂₆	File:8-simplex t036.svg t₀₃₆	File:8-simplex t136.svg t₁₃₆	File:8-simplex t046.svg t₀₄₆	File:8-simplex t056.svg t₀₅₆
File:8-simplex t017.svg t₀₁₇	File:8-simplex t027.svg t₀₂₇	File:8-simplex t037.svg t₀₃₇	File:8-simplex t0123.svg t₀₁₂₃	File:8-simplex t0124.svg t₀₁₂₄	File:8-simplex t0134.svg t₀₁₃₄	File:8-simplex t0234.svg t₀₂₃₄	File:8-simplex t1234.svg t₁₂₃₄	File:8-simplex t0125.svg t₀₁₂₅	File:8-simplex t0135.svg t₀₁₃₅	File:8-simplex t0235.svg t₀₂₃₅	File:8-simplex t1235.svg t₁₂₃₅	File:8-simplex t0145.svg t₀₁₄₅	File:8-simplex t0245.svg t₀₂₄₅	File:8-simplex t1245.svg t₁₂₄₅
File:8-simplex t0345.svg t₀₃₄₅	File:8-simplex t1345.svg t₁₃₄₅	File:8-simplex t2345.svg t₂₃₄₅	File:8-simplex t0126.svg t₀₁₂₆	File:8-simplex t0136.svg t₀₁₃₆	File:8-simplex t0236.svg t₀₂₃₆	File:8-simplex t1236.svg t₁₂₃₆	File:8-simplex t0146.svg t₀₁₄₆	File:8-simplex t0246.svg t₀₂₄₆	File:8-simplex t1246.svg t₁₂₄₆	File:8-simplex t0346.svg t₀₃₄₆	File:8-simplex t1346.svg t₁₃₄₆	File:8-simplex t0156.svg t₀₁₅₆	File:8-simplex t0256.svg t₀₂₅₆	File:8-simplex t1256.svg t₁₂₅₆
File:8-simplex t0356.svg t₀₃₅₆	File:8-simplex t0456.svg t₀₄₅₆	File:8-simplex t0127.svg t₀₁₂₇	File:8-simplex t0137.svg t₀₁₃₇	File:8-simplex t0237.svg t₀₂₃₇	File:8-simplex t0147.svg t₀₁₄₇	File:8-simplex t0247.svg t₀₂₄₇	File:8-simplex t0347.svg t₀₃₄₇	File:8-simplex t0157.svg t₀₁₅₇	File:8-simplex t0257.svg t₀₂₅₇	File:8-simplex t0167.svg t₀₁₆₇	File:8-simplex t01234.svg t₀₁₂₃₄	File:8-simplex t01235.svg t₀₁₂₃₅	File:8-simplex t01245.svg t₀₁₂₄₅	File:8-simplex t01345.svg t₀₁₃₄₅
File:8-simplex t02345.svg t₀₂₃₄₅	File:8-simplex t12345.svg t₁₂₃₄₅	File:8-simplex t01236.svg t₀₁₂₃₆	File:8-simplex t01246.svg t₀₁₂₄₆	File:8-simplex t01346.svg t₀₁₃₄₆	File:8-simplex t02346.svg t₀₂₃₄₆	File:8-simplex t12346.svg t₁₂₃₄₆	File:8-simplex t01256.svg t₀₁₂₅₆	File:8-simplex t01356.svg t₀₁₃₅₆	File:8-simplex t02356.svg t₀₂₃₅₆	File:8-simplex t12356.svg t₁₂₃₅₆	File:8-simplex t01456.svg t₀₁₄₅₆	File:8-simplex t02456.svg t₀₂₄₅₆	File:8-simplex t03456.svg t₀₃₄₅₆	File:8-simplex t01237.svg t₀₁₂₃₇
File:8-simplex t01247.svg t₀₁₂₄₇	File:8-simplex t01347.svg t₀₁₃₄₇	File:8-simplex t02347.svg t₀₂₃₄₇	File:8-simplex t01257.svg t₀₁₂₅₇	File:8-simplex t01357.svg t₀₁₃₅₇	File:8-simplex t02357.svg t₀₂₃₅₇	File:8-simplex t01457.svg t₀₁₄₅₇	File:8-simplex t01267.svg t₀₁₂₆₇	File:8-simplex t01367.svg t₀₁₃₆₇	File:8-simplex t012345.svg t₀₁₂₃₄₅	File:8-simplex t012346.svg t₀₁₂₃₄₆	File:8-simplex t012356.svg t₀₁₂₃₅₆	File:8-simplex t012456.svg t₀₁₂₄₅₆	File:8-simplex t013456.svg t₀₁₃₄₅₆	File:8-simplex t023456.svg t₀₂₃₄₅₆
File:8-simplex t123456.svg t₁₂₃₄₅₆	File:8-simplex t012347.svg t₀₁₂₃₄₇	File:8-simplex t012357.svg t₀₁₂₃₅₇	File:8-simplex t012457.svg t₀₁₂₄₅₇	File:8-simplex t013457.svg t₀₁₃₄₅₇	File:8-simplex t023457.svg t₀₂₃₄₅₇	File:8-simplex t012367.svg t₀₁₂₃₆₇	File:8-simplex t012467.svg t₀₁₂₄₆₇	File:8-simplex t013467.svg t₀₁₃₄₆₇	File:8-simplex t012567.svg t₀₁₂₅₆₇	File:8-simplex t0123456 A7.svg t_0123456	File:8-simplex t0123457 A7.svg t_0123457	File:8-simplex t0123467 A7.svg t_0123467	File:8-simplex t0123567 A7.svg t_0123567	File:8-simplex t01234567 A7.svg t_01234567

Notes

↑ Klitizing, (x3x3o3o3o3o3o3o - tene)
↑ Klitizing, (o3x3x3o3o3o3o3o - batene)
↑ Klitizing, (o3o3x3x3o3o3o3o - tatene)
↑ Klitizing, (o3o3o3x3x3o3o3o - be)

References

H.S.M. Coxeter:
- H.S.M. Coxeter, Regular Polytopes, 3rd Edition, Dover New York, 1973
- 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 22) H.S.M. Coxeter, Regular and Semi Regular Polytopes I, [Math. Zeit. 46 (1940) 380-407, MR 2,10]
  - (Paper 23) H.S.M. Coxeter, Regular and Semi-Regular Polytopes II, [Math. Zeit. 188 (1985) 559-591]
  - (Paper 24) H.S.M. Coxeter, Regular and Semi-Regular Polytopes III, [Math. Zeit. 200 (1988) 3-45]
Norman Johnson Uniform Polytopes, Manuscript (1991)
- N.W. Johnson: The Theory of Uniform Polytopes and Honeycombs, Ph.D.
Klitzing, Richard. "8D uniform polytopes (polyzetta)". x3x3o3o3o3o3o3o - tene, o3x3x3o3o3o3o3o - batene, o3o3x3x3o3o3o3o - tatene, o3o3o3x3x3o3o3o - be

External links

v t e Fundamental convex regular and uniform polytopes in dimensions 2–10
Family	A_n	B_n	I₂(p) / D_n	E₆ / E₇ / E₈ / F₄ / G₂	H_n
Regular polygon	Triangle	Square	p-gon	Hexagon	Pentagon
Uniform polyhedron	Tetrahedron	Octahedron • Cube	Demicube		Dodecahedron • Icosahedron
Uniform polychoron	Pentachoron	16-cell • Tesseract	Demitesseract	24-cell	120-cell • 600-cell
Uniform 5-polytope	5-simplex	5-orthoplex • 5-cube	5-demicube
Uniform 6-polytope	6-simplex	6-orthoplex • 6-cube	6-demicube	1₂₂ • 2₂₁
Uniform 7-polytope	7-simplex	7-orthoplex • 7-cube	7-demicube	1₃₂ • 2₃₁ • 3₂₁
Uniform 8-polytope	8-simplex	8-orthoplex • 8-cube	8-demicube	1₄₂ • 2₄₁ • 4₂₁
Uniform 9-polytope	9-simplex	9-orthoplex • 9-cube	9-demicube
Uniform 10-polytope	10-simplex	10-orthoplex • 10-cube	10-demicube
Uniform n-polytope	n-simplex	n-orthoplex • n-cube	n-demicube	1_k2 • 2_k1 • k₂₁	n-pentagonal polytope
Topics: Polytope families • Regular polytope • List of regular polytopes and compounds

[1] Klitizing, (x3x3o3o3o3o3o3o - tene)

[2] Klitizing, (o3x3x3o3o3o3o3o - batene)

[3] Klitizing, (o3o3x3x3o3o3o3o - tatene)

[4] Klitizing, (o3o3o3x3x3o3o3o - be)

[1]

[2]

[3]

[4]

Truncated 8-simplexes

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