Great inverted disnub icosidodecahedron

Great inverted disnub icosidodecahedron
(OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Gidsid
Elements
Components	2 great inverted snub icosidodecahedra
Faces	120 triangles, 40 triangles as 20 hexagrams, 24 pentagrams as 12 stellated decagrams
Edges	60+120+120
Vertices	120
Vertex figure	Irregular pentagon, edge lengths 1, 1, 1, 1, (√5–1)/2
Measures (edge length 1)
Circumradius	≈ 0.64502
Volume	≈ 5.42774
Dihedral angles	3–3: ≈ 89.78760°
	5/2–3: ≈ 21.61047°
Central density	26
Number of external pieces	1560
Level of complexity	100
Related polytopes
Army	Semi-uniform Grid
Regiment	Gidsid
Dual	Compound of two great inverted pentagonal hexecontahedra
Conjugates	Disnub icosidodecahedron, great disnub icosidodecahedron, great diretrosnub icosidodecahedron
Convex core	Order-6-truncated disdyakis triacontahedron
Abstract & topological properties
Flag count	1200
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The great inverted disnub icosidodecahedron, gidsid, or compound of two great inverted snub 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 snub icosidodecahedral antiprism, which is four-dimensional.

Measures

The circumradius $R \approx 0.64502$ of the great inverted disnub icosidodecahedron with unit edge length is the second to smallest positive real root of:

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

Its volume $V \approx 5.42775$ is given by the third largest 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" (#73).

• Klitzing, Richard. "gidsid".

• Wikipedia Contributors. "Compound of two great inverted snub icosidodecahedra".