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

More information Ak Coxeter plane, A8 ...

orthographic projections

Ak Coxeter plane	A8	A7	A6	A5
Graph
Dihedral symmetry	[9]	[8]	[7]	[6]
Ak Coxeter plane	A4	A3	A2
Graph
Dihedral symmetry	[5]	[4]	[3]

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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

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

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.

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Related polytopes

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Isotopic uniform truncated simplices

Dim.	2	3	4	5	6	7	8
Name Coxeter	Hexagon = t{3} = {6}	Octahedron = r{3,3} = {31,1} = {3,4} ${\displaystyle \left\{{\begin{array}{l}3\\3\end{array}}\right\}}$	Decachoron 2t{33}	Dodecateron 2r{34} = {32,2} ${\displaystyle \left\{{\begin{array}{l}3,3\\3,3\end{array}}\right\}}$	Tetradecapeton 3t{35}	Hexadecaexon 3r{36} = {33,3} ${\displaystyle \left\{{\begin{array}{l}3,3,3\\3,3,3\end{array}}\right\}}$	Octadecazetton 4t{37}
Images
Vertex figure	( )∨( )	{ }×{ }	{ }∨{ }	{3}×{3}	{3}∨{3}	{3,3}×{3,3}	{3,3}∨{3,3}
Facets		{3}	t{3,3}	r{3,3,3}	2t{3,3,3,3}	2r{3,3,3,3,3}	3t{3,3,3,3,3,3}
As intersecting dual simplexes	∩	∩	∩	∩	∩	∩	∩

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