# Icositetrachoric prism: Difference between revisions

Icositetrachoric prism
File:Icositetrachoric prism.png
Rank5
TypeUniform
Notation
Bowers style acronymIcope
Coxeter diagramx x3o4o3o ()
Elements
Tera24 octahedral prisms, 2 icositetrachora
Cells96 triangular prisms, 48 octahedra
Faces192 triangles, 96 squares
Edges24+192
Vertices48
Vertex figureCubic pyramid, edge lengths 1 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {5}}{2}}\approx 1.11803}$
Hypervolume2
Diteral anglesOpe–trip–ope: 120°
Ico–oct–ope: 90°
Height1
Central density1
Number of external pieces26
Level of complexity5
Related polytopes
ArmyIcope
RegimentIcope
DualIcositetrachoric tegum
ConjugateNone
Abstract & topological properties
Flag count11520
Euler characteristic2
OrientableYes
Properties
SymmetryF4×A1, order 2304
ConvexYes
NatureTame

The icositetrachoric prism or icope is a prismatic uniform polyteron that consists of 2 icositetrachora and 24 octahedral prisms. 1 icositetrachoron and 6 octahedral prisms join at each vertex. As the name suggests, it is a prism based on the icositetrachoron, which also makes it a convex segmentoteron.

The icositetrachoric prism contains the vertices of a regular penteract.

## Vertex coordinates

The vertices of an icositetrachoric prism of edge length 1 are given by all permutations and sign changes of the first four coordinates of:

• ${\displaystyle \left(\pm {\frac {\sqrt {2}}{2}},\,\pm {\frac {\sqrt {2}}{2}},\,0,\,0,\,\pm {\frac {1}{2}}\right).}$