Truncated icositetrachoric tetracomb

Truncated icositetrachoric tetracomb
Rank	5
Type	Uniform
Space	Euclidean
Notation
Bowers style acronym	Ticot
Coxeter diagram	x3x4o3o3o ()
Elements
Tera	3N tesseracts, N truncated icositetrachora
Cells	24N cubes, 12N truncated octahedra
Faces	72N squares, 32N hexagons
Edges	24N+96N
Vertices	48N
Vertex figure	Tetrahedral pyramid, edge lengths √2 (base) and √3 (sides)
Related polytopes
Army	Ticot
Regiment	Ticot
Conjugate	None
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	U5
Convex	Yes

The truncated icositetrachoric tetracomb, or ticot, is a convex uniform tetracomb. 4 truncated icositetrachora and 1 tesseract join at each vertex of this tessellation. As the name suggests, it is the truncation of the icositetrachoric tetracomb.

Vertex coordinates

The vertices of a truncated icositetrachoric tetracomb of edge length 1 are given by all permutations of:

• $\left(3\sqrt2i,\,±\frac{\sqrt2}{2}+3\sqrt2j,\,±\sqrt2+3\sqrt2k,\,±\frac{3\sqrt2}{2}+3\sqrt2l\right),$

where i, j, k, and l range over the integers.

Representations

A truncated icositetrachoric tetracomb has the following Coxeter diagrams:

• x3x4o3o3o (full symmetry)
• o3o4x3x3x (as great rhombated hexadecachoric tetracomb)
• o4x3x3x4o (as great birhombated tesseractic tetracomb)
• x3x3x *b3o4o (demitesseractic tetracomb symmetry)
• x3x3x *b3x *b3x (omnitruncate with quartertesseractic symmetry)

External links

• Klitzing, Richard. "ticot".

• Wikipedia Contributors. "Truncated 24-cell honeycomb".