# Disnub icosahedron

Disnub icosahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymDasi
Elements
Components20 octahedra
Faces40+120 triangles
Edges120+120
Vertices60
Vertex figureStellated octagon, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt2}{2} \approx 0.70711}$
Inradius${\displaystyle \frac{\sqrt6}{6} \approx 0.40825}$
Volume${\displaystyle \frac{20\sqrt2}{3} \approx 9.42809}$
Dihedral angle${\displaystyle \arccos\left(-\frac13\right) \approx 109.47122^\circ}$
Central density20
Related polytopes
ArmySemi-uniform Srid
RegimentGidrid
DualCompound of twenty cubes
ConjugateDisnub icosahedron
Convex coreIcosatruncated disdyakis triacontahedron
Abstract properties
Schläfli type{3,4}
Topological properties
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

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 = ${\displaystyle \arccos\left(\sqrt{\frac{-1+3\sqrt5+3\sqrt{-22+10\sqrt5}}{8}}\right) \approx 14.33033^\circ}$. It has the same edges as the uniform great dirhombicosidodecahedron.

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

## Vertex coordinates

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

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