Retrosnub disicositetrachoron

Retrosnub disicositetrachoron
Rank4
TypeUniform
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${\displaystyle {\frac {{\sqrt {5}}-1}{2}}\approx 0.61803}$
Hypervolume${\displaystyle 5{\frac {9-4{\sqrt {5}}}{4}}\approx 0.069660}$
Dichoral anglesGike–3–gike: 120°
Tet–3–tet: ${\displaystyle \arccos \left({\frac {3{\sqrt {5}}-1}{8}}\right)\approx 44.47751^{\circ }}$
Gike–3–tet: ${\displaystyle \arccos \left({\frac {\sqrt {10}}{4}}\right)\approx 37.76124^{\circ }}$
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:

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

Related polychora

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