Top Qs
Timeline
Chat
Perspective

Truncated 8-cubes

Convex uniform 8-polytope in 8-dimensional geometry From Wikipedia, the free encyclopedia

Remove ads

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

More information Orthogonal projections in B8 Coxeter plane ...

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

Remove ads

Truncated 8-cube

Truncated 8-cube
Typeuniform 8-polytope
Schläfli symbolt{4,3,3,3,3,3,3}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure( )v{3,3,3,3,3}
Coxeter groupsB8, [3,3,3,3,3,3,4]
Propertiesconvex

Alternate names

  • Truncated octeract (acronym tocto) (Jonathan Bowers)[1]

Coordinates

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

(±2,±2,±2,±2,±2,±2,±1,0)

Images

More information B8, B7 ...

The truncated 8-cube, is seventh in a sequence of truncated hypercubes:

Remove ads

Bitruncated 8-cube

More information Bitruncated 8-cube ...

Alternate names

  • Bitruncated octeract (acronym bato) (Jonathan Bowers)[2]

Coordinates

Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of

(±2,±2,±2,±2,±2,±1,0,0)

Images

More information B8, B7 ...

The bitruncated 8-cube is sixth in a sequence of bitruncated hypercubes:

More information Image, Name ...
Remove ads

Tritruncated 8-cube

More information Tritruncated 8-cube ...

Alternate names

  • Tritruncated octeract (acronym tato) (Jonathan Bowers)[3]

Coordinates

Cartesian coordinates for the vertices of a truncated 8-cube, centered at the origin, are all the sign coordinate permutations of

(±2,±2,±2,±2,±1,0,0,0)

Images

More information B8, B7 ...

Quadritruncated 8-cube

More information Quadritruncated 8-cube ...

Alternate names

  • Quadritruncated octeract (acronym oke) (Jonathan Bowers)[4]

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,±2,±1,0,0,0)

Images

More information B8, B7 ...
More information Dim., n ...
Remove ads

Notes

Loading content...

References

Loading content...
Loading related searches...

Wikiwand - on

Seamless Wikipedia browsing. On steroids.

Remove ads