Octahemioctahedral prism

The octahemioctahedral prism or ohope is a prismatic uniform polychoron that consists of 2 octahemioctahedra, 8 triangular prisms, and 4 hexagonal prisms. Each vertex joins 1 octahemioctahedron, 2 triangular prisms, and 2 hexagonal prisms. As the name suggests, it is a prism based on the octahemioctahedron.

Octahemioctahedral prism
(OFF file)
Rank	4
Type	Uniform
Notation
Bowers style acronym	Ohope
Coxeter diagram	x x3/2o3x3*b ()
Elements
Cells	8 triangular prisms, 4 hexagonal prisms, 2 octahemioctahedra
Faces	16 triangles, 24 squares, 8 hexagons
Edges	12+48
Vertices	24
Vertex figure	Bowtie pyramid, edge lengths 1, √3 (base), √2 (legs)
Measures (edge length 1)
Circumradius	${\frac {\sqrt {5}}{2}}\approx 1.11803$
Hypervolume	0
Dichoral angles	Oho–3–trip: 90°
	Oho–6–hip: 90°
	Trip–4–hip: $\arccos \left({\frac {1}{3}}\right)\approx 70.52878^{\circ }$
Height	1
Central density	0
Number of external pieces	48
Related polytopes
Army	Cope
Regiment	Cope
Dual	Octahemioctacronic bipyramid
Conjugate	None
Abstract & topological properties
Flag count	768
Euler characteristic	–2
Orientable	Yes
Properties
Symmetry	B3×A1, order 96
Convex	No
Nature	Tame

Vertex coordinates

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

External links

• Bowers, Jonathan. "Category 19: Prisms" (#909).

• Klitzing, Richard. "ohope".