Rectified hexacosichoric prism

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Rectified hexacosichoric prism
File:Rectified hexacosichoric prism.png
Rank5
TypeUniform
Notation
Bowers style acronymRoxip
Coxeter diagramx o5o3x3o ()
Elements
Tera600 octahedral prisms, 120 icosahedral prisms, 2 rectified hexacosichora
Cells1200+2400 triangular prisms, 1200 octahedra, 240 icosahedra
Faces2400+4800 triangles, 3600 squares
Edges720+7200
Vertices1440
Vertex figurePentagonal prismatic pyramid, edge lengths 1 (base), (legs)
Measures (edge length 1)
Circumradius
Hypervolume
Diteral anglesOpe–trip–ope:
 Ipe–trip–ope:
 Rox–ike–ipe: 90°
 Rox–oct–ope: 90°
Height1
Central density1
Number of external pieces722
Level of complexity15
Related polytopes
ArmyRoxip
RegimentRoxip
DualJoined hecatonicosachoric tegum
ConjugateRectified grand hexacosichoric prism
Abstract & topological properties
Euler characteristic2
OrientableYes
Properties
SymmetryH4×A1, order 28800
ConvexYes
NatureTame

The rectified hexacosichoric prism or roxip is a prismatic uniform polyteron that consists of 2 rectified hexacosichora, 120 icosahedral prisms, and 600 octahedral prisms. 1 rectified hexacosichoron, 2 icosahedral prisms, and 5 octahedral prisms join at each vertex. As the name suggests, it is a prism based on the rectified hexacosichoron, which also makes it a convex segmentoteron.

Vertex coordinates[edit | edit source]

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

along with even permutations of the first four coordinates of:

External links[edit | edit source]