# Octahemioctahedral prism

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Octahemioctahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymOhope
Coxeter diagramx x3/2o3x3*b ()
Elements
Cells8 triangular prisms, 4 hexagonal prisms, 2 octahemioctahedra
Faces16 triangles, 24 squares, 8 hexagons
Edges12+48
Vertices24
Vertex figureBowtie pyramid, edge lengths 1, 3 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt5}{2} ≈ 1.11803}$
Hypervolume0
Dichoral anglesOho–3–trip: 90°
Oho–6–hip: 90°
Trip–4–hip: ${\displaystyle \arccos\left(\frac13\right) ≈ 70.52878°}$
Height1
Central density0
Number of external pieces48
Related polytopes
ArmyCope
RegimentCope
DualOctahemioctacronic bipyramid
ConjugateNone
Abstract & topological properties
Euler characteristic–2
OrientableYes
Properties
SymmetryB3×A1, order 96
ConvexNo
NatureTame

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.

## Vertex coordinates

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