# Compound of two great icosahedra

Compound of two great icosahedra
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymSirsido
Elements
Components2 great icosahedra
Faces24 triangles, 16 triangles as 8 hexagrams
Edges12+48
Vertices24
Vertex figureRegular pentagram, edge length 1
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5-\sqrt5}{8}} \approx 0.58779}$
Inradius${\displaystyle \frac{3\sqrt3-\sqrt{15}}{12} \approx 0.11026}$
Volume${\displaystyle 5\frac{3-\sqrt5}{6} \approx 0.63661}$
Dihedral angle${\displaystyle \arccos\left(\frac{\sqrt5}{3}\right) \approx 41.81031^\circ}$
Central density14
Number of external pieces264
Level of complexity36
Related polytopes
ArmySemi-uniform Toe, edge lengths ${\displaystyle \frac{\sqrt{10}-\sqrt2}{4}}$ (squares), ${\displaystyle \frac{3\sqrt2-\sqrt{10}}{4}}$ (between ditrigons)
RegimentPassipsido
DualCompound of two great stellated dodecahedra
ConjugateCompound of two icosahedra
Convex coreOctatruncated tetrakis hexahedron
Abstract & topological properties
Flag count240
OrientableYes
Properties
SymmetryB3, order 48
ConvexNo
NatureTame

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

It can be constructed from the pentagrammatic snub pseudodisoctahedron by replacing each small stellated dodecahedron with the great icosahedron with which it shares its edges.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the pentagrammatic snub pseudodisoctahedron.