Retrosnub disicositetrachoron

Retrosnub disicositetrachoron
(OFF file)
Rank	4
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Rasdi
Coxeter diagram
Elements
Cells	24+96 tetrahedra, 24 great icosahedra
Faces	96+96+288 triangles
Edges	144+288
Vertices	96
Vertex figure	Trireplenished 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 angles	Gike–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 density	23
Number of external pieces	9024
Level of complexity	974
Related polytopes
Army	Sadi
Regiment	Rasdi
Conjugate	Snub disicositetrachoron
Abstract & topological properties
Euler characteristic	0
Orientable	Yes
Properties
Symmetry	F4/2, order 576
Convex	No
Nature	Tame

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.

Gallery

• 

  Wireframe

• 

  Card with cell counts, verf, and cross-sections

• 

  Convex core, with 24 tetrahedra and 96 gyroelongated triangular pyramids

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.

External links

• Bowers, Jonathan. "Category 20: Miscellaneous" (#970).

• Klitzing, Richard. "rasdi".