Compound of two snub icosidodecadodecahedra

Compound of two snub icosidodecadodecahedra
(3D model) (OFF file)
Rank	3
Type	Uniform
Notation
Bowers style acronym	Desided
Elements
Components	2 snub icosidodecadodecahedra
Faces	120 triangles, 40 triangles as 20 hexagrams, 24 pentagons as 12 stellated decagons, 24 pentagrams as 12 stellated decagrams
Edges	120+120+120
Vertices	120
Vertex figure	Irregular hexagon, edge lengths 1, 1, 1, (√5–1)/2, 1, (1+√5)/2
Measures (edge length 1)
Circumradius	≈ 1.12690
Volume	≈ 29.28396
Dihedral angles	3–3: ≈ 146.78125°
	5–3: ≈ 120.43401°
	5/2–3: ≈ 7.35214°
Central density	8
Number of external pieces	752
Level of complexity	47
Related polytopes
Army	Semi-uniform Grid
Regiment	Desided
Dual	Compound of two medial hexagonal hexecontahedra
Conjugate	Compound of two snub icosidodecadodecahedra
Convex core	Dodecahedron
Abstract & topological properties
Flag count	1440
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The disnub icosidodecadodecahedron, desided, or compound of two snub icosidodecadodecahedra is a uniform polyhedron compound. It consists of 120 snub triangles, 40 further triangles, 24 pentagons, and 24 pentagrams (the latter three can combine in pairs due to faces in the same plane). Four triangles, one pentagon, and one pentagram join at each vertex.

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

Measures

The circumradius $R\approx 1.12690$ of the disnub icosidodecadodecahedron with unit edge length is the greatest real root of

$64x^{6}-128x^{4}+68x^{2}-11.$

Its volume $V\approx 29.28396$ is given by the positive real root of

$729x^{6}-622080x^{4}-162000x^{2}-2121800000.$

External links

• Bowers, Jonathan. "Polyhedron Category C10: Disnubs" (#74).

• Klitzing, Richard. "desided".

• Wikipedia contributors. "Compound of two snub icosidodecadodecahedra".