Compound of two great inverted retrosnub icosidodecahedra

Compound of two great inverted retrosnub icosidodecahedra
(OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidrissid
Elements
Components	2 great inverted retrosnub icosidodecahedra
Faces	120 triangles, 40 triangles as 20 hexagrams, 24 pentagrams as 12 stellated decagrams
Edges	60+120+120
Vertices	120
Vertex figure	Irregular pentagram, edge lengths 1, 1, 1, 1, (√5–1)/2
Measures (edge length 1)
Circumradius	≈ 0.58000
Volume	≈ 2.07520
Dihedral angles	5/2–3: ≈ 67.31029°
	3–3: ≈ 21.72466°
Central density	74
Number of external pieces	2580
Related polytopes
Army	Semi-uniform Grid
Regiment	Gidrissid
Dual	Compound of two great pentagrammic hexecontahedra
Conjugates	Compound of two snub dodecahedra, compound of two great snub icosidodecahedra, compound of two great inverted snub icosidodecahedra
Convex core	Order-6-truncated disdyakis triacontahedron
Abstract & topological properties
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The great diretrosnub icosidodecahedron, gidrissid, or compound of two great inverted retrosnub icosidodecahedra is a uniform polyhedron compound. It consists of 120 snub triangles, 40 further triangles, and 24 pentagrams (the latter two can combine in pairs due to faces in the same plane). Four triangles and one pentagram join at each vertex.

Its quotient prismatic equivalent is the great inverted retrosnub icosidodecahedral antiprism, which is four-dimensional.

Measures

The circumradius $R \approx 0.58000$ of the great diretrosnub icosidodecahedron with unit edge length is the smallest positive real root of:

$4096x^{12}-27648x^{10}+47104x^8-35776x^6+13872x^4-2696x^2+209.$

Its volume $V \approx 2.07520$ is given by the smallest positive real root of:

$\begin{align}&531441x^{12}-3120444405x^{10}+633684343500x^8+16101978406875x^6\\ {} &+384557737134375x^4-45531087887643750x^2+187445810737515625.\end{align}$

External links

• Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#75).

• Klitzing, Richard. "gidrissid".

• Wikipedia Contributors. "Compound of two great retrosnub icosidodecahedra".