Great icosidodecahedron

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Great icosidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymGid
Coxeter diagramo5/2x3o ()
Elements
Faces20 triangles, 12 pentagrams
Edges60
Vertices30
Vertex figureRectangle, edge lengths 1 and (5–1)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angle
Central density7
Number of external pieces132
Level of complexity10
Related polytopes
ArmyId, edge length
RegimentGid
DualGreat rhombic triacontahedron
ConjugateIcosidodecahedron
Convex coreIcosahedron
Abstract & topological properties
Flag count240
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryH3, order 120
Flag orbits2
ConvexNo
NatureTame

The great icosidodecahedron or gid is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagrams, with two of each joining at a vertex. It can be derived as a rectified great stellated dodecahedron or great icosahedron.

Vertex coordinates[edit | edit source]

A great icosidodecahedron of side length 1 has vertex coordinates given by all permutations of

  • ,

and even permutations of

  • .

The first set of vertices corresponds to a scaled octahedron which can be inscribed into the great icosidodecahedron.

Related polyhedra[edit | edit source]

The great icosidodecahedron is the colonel of a three-member regiment that also includes the great icosihemidodecahedron and great dodecahemidodecahedron.

External links[edit | edit source]