# Prismatorhombiretrosnub icositetrachoron

Prismatorhombiretrosnub icositetrachoron
Rank4
TypeScaliform
Notation
Bowers style acronymPrarsi
Coxeter diagram
Elements
Cells96 triangular prisms, 96 triangular cupolas, 24 truncated tetrahedra, 24 great icosahedra
Faces96+192+288 triangles, 288 squares, 96 hexagons
Edges144+288+576
Vertices288
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {4-{\sqrt {5}}}}\approx 1.32813}$
Hypervolume${\displaystyle {\frac {140{\sqrt {5}}-309}{4}}\approx 1.01238}$
Central density-1
Related polytopes
ArmyNon-equilateral Prissi
RegimentPrarsi
ConjugatePrismatorhombisnub icositetrachoron
Abstract & topological properties
OrientableYes
Properties
SymmetryF4/2, order 576
ConvexNo
NatureTame

The prismatorhombiretrosnub icositetrachoron, or prarsi, is a scaliform polychoron. It consists of 96 triangular prisms, 96 triangular cupolas, 24 truncated tetrahedra, and 24 great icosahedra. 1 great icosahedron, 1 truncated tetrahedron, 2 triangular prisms, and 3 triangular cupolas join at each vertex.

It can be constructed from the retrosnub disicositetrachoron by expanding the icosahedral cells outward by unit distance. It is also a subsymmetrical faceting of gidipthi; blending 25 of this polychoron results in gad phiddix, a member of the gidipthi regiment.

## Vertex coordinates

A prismatorhombiretrosnub icositetrachoron of edge length 1 has vertex coordinates given by all even permutations of:

• ${\displaystyle \left(0,\,\pm {\frac {1}{2}},\,\pm {\frac {1-{\sqrt {5}}}{4}},\,\pm {\frac {7-{\sqrt {5}}}{4}}\right),}$
• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm 1,\,\pm {\frac {3-{\sqrt {5}}}{4}},\,\pm {\frac {5-{\sqrt {5}}}{4}}\right).}$