# Retrosnub disicositetrachoron

Retrosnub disicositetrachoron Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymRasdi
Coxeter diagram         Elements
Cells24+96 tetrahedra, 24 great icosahedra
Faces96+96+288 triangles
Edges144+288
Vertices96
Vertex figureTrireplenished great icosahedron, edge length 1
Measures (edge length 1)
Circumradius$\frac{\sqrt5-1}{2} ≈ 0.61803$ Hypervolume$5\frac{9-4\sqrt5}{4} ≈ 0.069660$ Dichoral anglesGike–3–gike: 120°
Tet–3–tet: $\arccos\left(\frac{3\sqrt5-1}{8}\right) ≈ 44.47751°$ Gike–3–tet: $\arccos\left(\frac{\sqrt{10}}{4}\right) ≈ 37.76124°$ Central density23
Number of external pieces9024
Level of complexity974
Related polytopes
RegimentRasdi
ConjugateSnub disicositetrachoron
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryF4/2, order 576
ConvexNo
NatureTame

The retrosnub disicositetrachoron, or rasdi, is a nonconvex uniform polychoron that consists of 24+96 regular tetrahedra and 24 great icosahedra. 5 tetrahedra and 3 great icosahedra join at each vertex.

It is related to the grand hexacosichoron in a similar way as the snub disicositetrachoron is to the regular hexacosichoron, with the great icosahedra being vertex figures of the grand hexacosichoron.

## Vertex coordinates

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

• $\left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{4},\,±\frac12,\,0\right).$ ## Related polychora

The retrosnub disicositetrachoron's regiment also contains a coincidic scaliform polychoron, the icositetradiminished great faceted hexacosichoron.