Retroantiprismatosnub disicositetrachoron

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Retroantiprismatosnub disicositetrachoron
Rank4
TypeUniform
Notation
Bowers style acronymRappisdi
Elements
Cells96 octahedra, 24 icosahedra, 24 great icosahedra
Faces96+192+288+288 triangles
Edges144+576
Vertices96
Vertex figureDisrhombitritrihedron, edge length 1
Measures (edge length 1)
Circumradius1
Hypervolume
Dichoral anglesGike–3–oct:
 Oct–3–oct: 120°
 Gike–3–ike: 60°
 Ike–3–oct:
Number of external pieces6552
Level of complexity571
Related polytopes
ArmySadi
RegimentRappisdi
ConjugateRetroantiprismatosnub disicositetrachoron
Convex coreIcositetrachoron
Abstract & topological properties
Euler characteristic96
OrientableYes
Properties
SymmetryF4/2, order 576
ConvexNo
NatureTame

The retroantiprismatosnub disicositetrachoron, or rappisdi, is a nonconvex uniform polychoron that consists of 96 regular octahedra, 24 icosahedra, and 24 great icosahedra. 6 octahedra, 3 icosahedra, and 3 great icosahedra join at each vertex.

This polychoron has the same symmetry as the snub disicositetrachoron, with the octahedra acting as triangular antifrusta. It can be thought as a partial faceting of the small stellated hecatonicosachoron.

Cross-sections[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a retroantiprismatosnub disicositetrachoron of edge length 1, centered at the origin, are given by all even permutations of:

Related polychora[edit | edit source]

The retroantiprismatosnub disicositetrachoron shares its vertices and edges with the small retrohemiantiprismatosnub prismatodisicositetrachoron and great retrohemiantiprismatosnub prismatodisicositetrachoron.

External links[edit | edit source]