# Compound of two icosahedra

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Compound of two icosahedra
Rank3
TypeUniform
Notation
Bowers style acronymSiddo
Coxeter diagramo4ß3ß ()
Elements
Components2 icosahedra
Faces24 triangles, 16 triangles as 8 hexagrams
Edges12+48
Vertices24
Vertex figureRegular pentagon, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {5+{\sqrt {5}}}{8}}}\approx 0.95106}$
Inradius${\displaystyle {\frac {3{\sqrt {3}}+{\sqrt {15}}}{12}}\approx 0.75576}$
Volume${\displaystyle 5{\frac {3+{\sqrt {5}}}{6}}\approx 4.36339}$
Dihedral angle${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{3}}\right)\approx 138.18969^{\circ }}$
Central density2
Number of external pieces80
Level of complexity13
Related polytopes
ArmySemi-uniform Toe, edge lengths ${\displaystyle {\frac {\sqrt {2}}{2}}}$ (squares), ${\displaystyle {\frac {{\sqrt {10}}-{\sqrt {2}}}{4}}}$ (between ditrigons)
RegimentSiddo
DualCompound of two dodecahedra
ConjugateCompound of two great icosahedra
Convex coreOrder-6 truncated tetrakis hexahedron
Abstract & topological properties
Flag count240
Schläfli type{3,5}
OrientableYes
Properties
SymmetryB3, order 48
Flag orbits5
ConvexNo
NatureTame

The snub disoctahedron, siddo, or compound of two icosahedra is a uniform polyhedron compound. It consists of 40 triangles (8 pairs of which form hexagrams due to falling in the same plane), with five faces joining at a vertex.

The icosahedra have pyritohedral symmetry, and can be seen as two forms of alternation of the semi-uniform truncated octahedron that is its convex hull.

Its quotient prismatic equivalent is the pyritohedral icosahedral antiprism, which is four-dimensional.

## Vertex coordinates

The vertices of a snub disoctahedron of edge length 1 can be given by all permutations of:

• ${\displaystyle \left(\pm {\frac {1+{\sqrt {5}}}{4}},\,\pm {\frac {1}{2}},\,0\right).}$