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	16 truncated 7-demicubes 128 truncated 7-simplexes 128 rectified 7-simplexes
6-faces	112 truncated 6-demicubes 1024 truncated 6-simplexes 1024 rectified 6-simplexes 1024 6-simplexes
5-faces	448 truncated 5-demicubes 3584 truncated 5-simplexes 3584 rectified 5-simplexes 7168 5-simplexes
4-faces	1120 truncated 16-cells 7168 truncated 5-cells 7168 rectified 5-cells 21504 5-cells
Cells	1792 truncated tetrahedra 8960 truncated tetrahedra 8960 octahedra 35840 tetrahedra
Faces	7168 hexagons 7168 triangles 35840 triangles
Edges	1792 segments 21504 segments
Vertices	3584
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]