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Truncated 8-orthoplexes

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In eight-dimensional geometry, a truncated 8-orthoplex is a convex uniform 8-polytope, being a truncation of the regular 8-orthoplex.

More information Orthogonal projections in B8 Coxeter plane ...

There are 7 truncation for the 8-orthoplex. Vertices of the truncation 8-orthoplex are located as pairs on the edge of the 8-orthoplex. Vertices of the bitruncated 8-orthoplex are located on the triangular faces of the 8-orthoplex. Vertices of the tritruncated 7-orthoplex are located inside the tetrahedral cells of the 8-orthoplex. The final truncations are best expressed relative to the 8-cube.

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Truncated 8-orthoplex

Truncated 8-orthoplex
Typeuniform 8-polytope
Schläfli symbolt0,1{3,3,3,3,3,3,4}
Coxeter-Dynkin diagrams

6-faces
5-faces
4-faces
Cells
Faces
Edges1456
Vertices224
Vertex figure( )v{3,3,3,4}
Coxeter groupsB8, [3,3,3,3,3,3,4]
D8, [35,1,1]
Propertiesconvex

Alternate names

  • Truncated octacross (acronym tek) (Jonthan Bowers)[1]

Construction

There are two Coxeter groups associated with the truncated 8-orthoplex, one with the C8 or [4,3,3,3,3,3,3] Coxeter group, and a lower symmetry with the D8 or [35,1,1] Coxeter group.

Coordinates

Cartesian coordinates for the vertices of a truncated 8-orthoplex, centered at the origin, are all 224 vertices are sign (4) and coordinate (56) permutations of

(±2,±1,0,0,0,0,0,0)

Images

More information B8, B7 ...
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Bitruncated 8-orthoplex

More information Bitruncated 8-orthoplex ...

Alternate names

  • Bitruncated octacross (acronym batek) (Jonthan Bowers)[2]

Coordinates

Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of

(±2,±2,±1,0,0,0,0,0)

Images

More information B8, B7 ...
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Tritruncated 8-orthoplex

More information Tritruncated 8-orthoplex ...

Alternate names

  • Tritruncated octacross (acronym tatek) (Jonthan Bowers)[3]

Coordinates

Cartesian coordinates for the vertices of a bitruncated 8-orthoplex, centered at the origin, are all sign and coordinate permutations of

(±2,±2,±2,±1,0,0,0,0)

Images

More information B8, B7 ...

Notes

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References

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