Great icosidodecahedron

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Great icosidodecahedron
Great icosidodecahedron.png
Bowers style acronymGid
Coxeter diagramo5/2x3o (CDel node.pngCDel 5-2.pngCDel node 1.pngCDel 3.pngCDel node.png)
Faces20 triangles, 12 pentagrams
Vertex figureRectangle, edge lengths 1 and (5–1)/2
Great icosidodecahedron vertfig.png
Measures (edge length 1)
Dihedral angle
Central density7
Number of pieces132
Level of complexity10
Related polytopes
DualGreat rhombic triacontahedron
Convex coreIcosahedron
Abstract properties
Euler characteristic2
Topological properties
SymmetryH3, order 120

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 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.

o3o5/2o truncations
Name OBSA Schläfli symbol CD diagram Picture
Great icosahedron gike {3,5/2} x3o5/2o (CDel node 1.pngCDel 3.pngCDel node.pngCDel 5-2.pngCDel node.png)
Great icosahedron.png
Truncated great icosahedron tiggy t{3,5/2} x3x5/2o (CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5-2.pngCDel node.png)
Great truncated icosahedron.png
Great icosidodecahedron gid r{3,5/2} o3x5/2o (CDel node.pngCDel 3.pngCDel node 1.pngCDel 5-2.pngCDel node.png)
Great icosidodecahedron.png
Truncated great stellated dodecahedron (degenerate, ike+2gad) t{5/2,3} o3x5/2x (CDel node.pngCDel 3.pngCDel node 1.pngCDel 5-2.pngCDel node 1.png)
Small complex icosidodecahedron.png
Great stellated dodecahedron gissid {5/2,3} o3o5/2x (CDel node.pngCDel 3.pngCDel node.pngCDel 5-2.pngCDel node 1.png)
Great stellated dodecahedron.png
Small complex rhombicosidodecahedron (degenerate, sidtid+rhom) sicdatrid rr{3,5/2} x3o5/2x (CDel node 1.pngCDel 3.pngCDel node.pngCDel 5-2.pngCDel node 1.png)
Compound of small ditrigonal icosidodecahedron and the compound of five cubes.png
Truncated great icosidodecahedron (degenerate, ri+12(10/2)) tr{3,5/2} x3x5/2x (CDel node 1.pngCDel 3.pngCDel node 1.pngCDel 5-2.pngCDel node 1.png)
Great snub icosidodecahedron gosid sr{3,5/2} s3s5/2s (CDel node h.pngCDel 3.pngCDel node h.pngCDel 5-2.pngCDel node h.png)
Great snub icosidodecahedron.png

External links[edit | edit source]

  • Klitzing, Richard. "gid".