Great icosidodecahedron

From Polytope Wiki
Jump to navigation Jump to search
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 external pieces132
Level of complexity10
Related polytopes
ArmyId, edge length
DualGreat rhombic triacontahedron
Convex coreIcosahedron
Abstract & topological properties
Flag count240
Euler characteristic2
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".