Disnub icosahedron

Disnub icosahedron
	(3D model); (OFF file)
Rank	3
Type	Uniform
Space	Spherical
Notation
Bowers style acronym	Dasi
Elements
Components	20 octahedra
Faces	40+120 triangles
Edges	120+120
Vertices	60
Vertex figure	Stellated octagon, edge length 1
Measures (edge length 1)
Circumradius
Inradius
Volume
Dihedral angle
Central density	20
Related polytopes
Army	Semi-uniform Srid
Regiment	Gidrid
Dual	Compound of twenty cubes
Conjugate	Disnub icosahedron
Convex core	Icosatruncated disdyakis triacontahedron
Abstract properties
Schläfli type	{3,4}
Topological properties
Orientable	Yes
Properties
Symmetry	H3, order 120
Convex	No
Nature	Tame

The disnub icosahedron, dasi, or compound of twenty octahedra is a uniform polyhedron compound. It consists of 40+120 triangles. The vertices coincide in pairs, and thus eight triangles join at each vertex.

This compound is a special case of the more general altered disnub icosahedron, with θ = $\arccos\left(\sqrt{\frac{-1+3\sqrt5+3\sqrt{-22+10\sqrt5}}{8}}\right) \approx 14.33033^\circ$ . It has the same edges as the uniform great dirhombicosidodecahedron.

Its quotient prismatic equivalent is the triangular antiprismatic icosayodakoorthowedge, which is 22-dimensional.

Gallery[edit | edit source]

Vertex coordinates[edit | edit source]

The vertices of a disnub icosahedron of edge length 1 are given by all even permutations of:

$\left(±\sqrt{\frac{\sqrt5-1-2\sqrt{\sqrt5-2}}{8}},\,±\sqrt{\frac{3-\sqrt5-\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2+\sqrt{2\sqrt5-2}}{8}}\right),$
$\left(0,\,±\frac{\sqrt{3-\sqrt5}}{2},\,±\frac{\sqrt{\sqrt5-1}}{2}\right),$
$\left(±\sqrt{\frac{3-\sqrt5+\sqrt{10\sqrt5-22}}{8}},\,±\sqrt{\frac{2-\sqrt{2\sqrt5-2}}{8}},\,±\sqrt{\frac{\sqrt5-1+2\sqrt{\sqrt5-2}}{8}}\right).$