Prismatorhombisnub icositetrachoron

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Prismatorhombisnub icositetrachoron
Rank4
TypeScaliform
Notation
Bowers style acronymPrissi
Coxeter diagrams3s4o3x ()
Elements
Cells96 triangular cupolas, 96 triangular prisms, 24 truncated tetrahedra, 24 icosahedra
Faces96+192+288 triangles, 288 squares, 96 hexagons
Edges144+288+576
Vertices288
Vertex figureDigonal-pentagonal wedge, pentagon edge length 1, other lateral edge lengths 1, 2, and 3
Measures (edge length 1)
Circumradius
Hypervolume
Dichoral anglesTrip–4–tricu:
 Tut–3–tricu:
 Tut–6–tricu:
 Ike–3–trip: 150°
 Ike–3–tricu:
Central density1
Related polytopes
ArmyPrissi
RegimentPrissi
DualDipentanotched diacosioctacontoctachoron
ConjugatePrismatorhombiretrosnub icositetrachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryF4/2, order 576
ConvexYes
NatureTame

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

It can be constructed from the snub disicositetrachoron by expanding the icosahedral cells outward by unit distance, or from the prismatorhombated icositetrachoron by alternating the triangles and equalizing edge lengths. It is also a subsymmetrical faceting of the prismatodishecatonicosachoron.

It contains the vertices of a pyritosnub tesseract with regular icosahedra and uniform triangular prisms.

Vertex coordinates[edit | edit source]

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

Representations[edit | edit source]

A prismatorhombisnub icositetrachoron has the following Coxeter diagrams:

  • s3s4o3x (full symmetry)
  • fox3xxx3xfo *b3oxf&#zx (D4 symmetry)

External links[edit | edit source]