Truncated tesseractihemioctachoron

Truncated tesseractihemioctachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Titho
Coxeter diagram	(x3x3x3o3/2*a)/2 (/2)
Elements
Cells	8 tetrahemihexahedra, 8 truncated tetrahedra, 4 truncated octahedra
Faces	32 triangles, 24 squares, 32 hexagons
Edges	24+96
Vertices	48
Vertex figure	Bowtie pyramid, base edge lengths 1 and √2, side edge length √3
Measures (edge length 1)
Circumradius	$\frac{\sqrt{10}}{2} \approx 1.58114$
Dichoral angles	Thah–3–tut: 120°
	Thah–4–toe: 90°
	Tut–6–toe: 60°
Number of external pieces	72
Level of complexity	17
Related polytopes
Army	Thex
Regiment	Thex
Conjugate	None
Abstract & topological properties
Orientable	No
Properties
Symmetry	D4, order 192
Convex	No
Nature	Tame

The truncated tesseractihemioctachoron, or titho, is a nonconvex uniform polychoron that consists of 8 tetrahemihexahedra, 8 truncated tetrahedra, and 4 truncated octahedra. One tetrahemihexahedron, two truncated tetrahedra, and two truncated octahedra join at each vertex. As the name suggests, it can be obtained by truncating the tesseractihemioctachoron.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the truncated hexadecachoron.

External links

• Bowers, Jonathan. "Category 2: Truncates" (#30).

• Klitzing, Richard. "titho".