Cantic 8-cube

In eight-dimensional geometry, a cantic 8-cube or truncated 8-demicube is a uniform 8-polytope, being a truncation of the 8-demicube.

Cantic 8-cube
D8 Coxeter plane projection
Type	uniform 8-polytope
Schläfli symbol	t0,1{3,35,1} h2{4,3,3,3,3,3,3}
Coxeter-Dynkin diagram
7-faces
6-faces
5-faces
4-faces
Cells
Faces
Edges
Vertices
Vertex figure	( )v{ }x{3,3,3,3}
Coxeter groups	D8, [35,1,1]
Properties	convex

Alternate names

• Truncated demiocteract
• Truncated hemiocteract; Acronym: thocto (Jonathan Bowers)^[1]

Cartesian coordinates

The Cartesian coordinates for the vertices of a truncated 8-demicube centered at the origin and edge length 6√2 are coordinate permutations:

(±1,±1,±3,±3,±3,±3,±3,±3)

with an odd number of plus signs.

Images

orthographic projections

Coxeter plane	B8	D8	D7	D6	D5
Graph
Dihedral symmetry	[16/2]	[14]	[12]	[10]	[8]
Coxeter plane	D4	D3	A7	A5	A3
Graph
Dihedral symmetry	[6]	[4]	[8]	[6]	[4]