Inverted disnub dodecadodecahedron

The inverted disnub dodecadodecahedron, idisdid, or compound of two inverted snub dodecadodecahedra is a uniform polyhedron compound. It consists of 120 snub triangles, 24 pentagons, and 24 pentagrams (the latter two can combine in pairs due to faces in the same plane). Three triangles, one pentagon, and one pentagram join at each vertex.

Inverted disnub dodecadodecahedron
(3D model) (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Idisdid
Elements
Components	2 inverted snub dodecadodecahedra
Faces	120 triangles, 24 pentagons as 12 stellated decagons, 24 pentagrams as 12 stellated decagrams
Edges	60+120+120
Vertices	120
Vertex figure	Irregular pentagon, edge lengths 1, 1, (√5–1)/2, 1, (1+√5)/2
Measures (edge length 1)
Circumradius	≈ 0.85163
Volume	≈ 9.22862
Dihedral angles	3–3: ≈ 130.49074°
	5–3: ≈ 68.64088
	5/2–3: ≈ 11.12448°
Central density	18
Number of external pieces	1752
Level of complexity	112
Related polytopes
Army	Semi-uniform Grid
Regiment	Idisdid
Dual	Compound of two medial inverted pentagonal hexecontahedra
Conjugate	Disnub dodecadodecahedron
Convex core	Dodecahedron
Abstract & topological properties
Flag count	1200
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

Its quotient prismatic equivalent is the inverted snub dodecadodecahedral antiprism, which is four-dimensional.

Measures

The circumradius $R \approx 0.85163$ of the inverted disnub dodecadodecahedron with unit edge length is the smallest positive real root of:

$64x^8-192x^6+180x^4-65x^2+8.$

Its volume $V \approx 9.22862$ is given by the smallest positive real root of:

$x^8-1340x^6+4525x^4+5895625x^2+240250000.$

External links

• Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#72).

• Klitzing, Richard. "idisdid".

• Wikipedia Contributors. "Compound of two inverted snub dodecadodecahedra".