Tetrahemihexahedral prism

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Tetrahemihexahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Thahp
Coxeter diagram	(x x3/2o3x)/2 ()/2
Elements
Cells	4 triangular prisms, 3 cubes, 2 tetrahemihexahedra
Faces	8 triangles, 6+12 squares
Edges	6+24
Vertices	12
Vertex figure	Bowtie pyramid, edge lengths 1 and √2 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {3}}{2}}\approx 0.86603$
Dichoral angles	Thah–3–trip: 90°
	Thah–4–cube: 90°
	Trip–4–cube: $\arccos \left({\frac {\sqrt {3}}{3}}\right)\approx 54.73561^{\circ }$
Height	1
Number of external pieces	24
Related polytopes
Army	Ope
Regiment	Ope
Dual	Tetrahemihexacronic tegum
Conjugate	None
Abstract & topological properties
Flag count	384
Euler characteristic	–1
Orientable	No
Properties
Symmetry	A3×A1, order 48
Convex	No
Nature	Tame

The tetrahemihexahedral prism or thahp is a prismatic uniform polychoron that consists of 2 tetrahemihexahedra, 4 triangular prisms, and 3 cubes. Each vertex joins 1 tetrahemihexahedron, 4 triangular prisms, and 3 cubes. As the name suggests, it is a prism based on the tetrahemihexahedron.

Cross-sections

Vertex coordinates

Its vertices are the same as those of its regiment colonel, the octahedral prism.

External links

• Bowers, Jonathan. "Category 19: Prisms" (#897).

• Klitzing, Richard. "thahp".