Hexacosichoric prism

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Hexacosichoric prism
File:Hexacosichoric prism.png
Rank5
TypeUniform
Notation
Bowers style acronymExip
Coxeter diagramx o5o3o3x ()
Elements
Tera600 tetrahedral prisms, 2 hexacosichora
Cells1200 tetrahedra, 1200 triangular prisms
Faces2400 triangles, 720 squares
Edges120+1440
Vertices240
Vertex figureIcosahedral pyramid, edge lengths 1 (base), 2 (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesTepe–trip–tepe:
 Ex–tet–tepe: 90°
Height1
Central density1
Number of external pieces602
Level of complexity5
Related polytopes
ArmyExip
RegimentExip
DualHecatonicosachoric tegum
ConjugateGrand hexacosichoric prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH4×A1, order 28800
ConvexYes
NatureTame

The hexacosichoric prism or exip is a prismatic uniform polyteron that consists of 2 hexacosichora and 600 tetrahedral prisms. 1 hexacosichoron and 20 tetrahedral prisms join at each vertex. As the name suggests, it is a prism based on the hexacosichoron, which also makes it a convex segmentoteron.

Vertex coordinates[edit | edit source]

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

together with all the even permutations of the first four coordinates of:

External links[edit | edit source]