Disnub dodecadodecahedron

Disnub dodecadodecahedron
(OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Disdid
Elements
Components	2 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	≈ 1.27444
Volume	≈ 36.51284
Dihedral angles	5–3: ≈ 157.77792°
	3–3: ≈ 151.48799°
	5/2–3: ≈ 129.79515°
Central density	6
Number of external pieces	1092
Level of complexity	64
Related polytopes
Army	Semi-uniform Grid
Regiment	Disdid
Dual	Compound of two medial pentagonal hexecontahedra
Conjugate	Inverted disnub dodecadodecahedron
Abstract & topological properties
Flag count	1200
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The disnub dodecadodecahedron, disdid, or compound of two 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.

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

Measures

The circumradius $R \approx 1.27444$ of the disnub dodecadodecahedron with unit edge length is the largest real root of:

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

Its volume $V \approx 36.51284$ is given by the largest real root of:

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

External links

• Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#70).

• Klitzing, Richard. "disdid".

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