Truncated 8-orthoplex


8-orthoplex

Truncated 8-orthoplex

Bitruncated 8-orthoplex

Tritruncated 8-orthoplex

Quadritruncated 8-cube

8-cube

Truncated 8-cube

Bitruncated 8-cube

Tritruncated 8-cube
Orthogonal projections in BC8 Coxeter plane

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

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.

Contents


Truncated 8-orthoplex

Truncated 8-orthoplex
Type uniform polyzetton
Schläfli symbol t0,1{3,3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges 1456
Vertices 224
Vertex figure Elongated 6-orthoplex pyramid
Coxeter groups BC8, [3,3,3,3,3,3,4]
D8, [35,1,1]
Properties convex

Alternate names

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

orthographic projections
B8 B7
[16] [14]
B6 B5
[12] [10]
B4 B3 B2
[8] [6] [4]
A7 A5 A3
[8] [6] [4]

Bitruncated 8-orthoplex

Bitruncated 8-orthoplex
Type uniform polyzetton
Schläfli symbol t1,2{3,3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups BC8, [3,3,3,3,3,3,4]
D8, [35,1,1]
Properties convex

Alternate names

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

orthographic projections
B8 B7
[16] [14]
B6 B5
[12] [10]
B4 B3 B2
[8] [6] [4]
A7 A5 A3
[8] [6] [4]

Tritruncated 8-orthoplex

Tritruncated 8-orthoplex
Type uniform polyzetton
Schläfli symbol t2,3{3,3,3,3,3,3,4}
Coxeter-Dynkin diagrams
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure
Coxeter groups BC8, [3,3,3,3,3,3,4]
D8, [35,1,1]
Properties convex

Alternate names

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

orthographic projections
B8 B7
[16] [14]
B6 B5
[12] [10]
B4 B3 B2
[8] [6] [4]
A7 A5 A3
[8] [6] [4]

Notes

  1. ^ Klitizing, (x3x3o3o3o3o3o4o - tek)
  2. ^ Klitizing, (o3x3x3o3o3o3o4o - batek)
  3. ^ Klitizing, (o3o3x3x3o3o3o4o - tatek)

References

External links