Great inverted snub icosidodecahedron

The great inverted snub icosidodecahedron or gisid, is a uniform polyhedron. It consists of 60 snub triangles, 20 additional triangles, and 12 pentagrams. Four triangles and one pentagram meet at each vertex. It can be constructed by alternation of the great quasitruncated icosidodecahedron after setting all edge lengths to be equal.

Great inverted snub icosidodecahedron
Great inverted snub icosidodecahedron.png
Bowers style acronymGisid
Coxeter diagrams5/3s3s (CDel node h.pngCDel 5.pngCDel rat.pngCDel 3x.pngCDel node h.pngCDel 3.pngCDel node h.png)
Faces20+60 triangles, 12 pentagrams
Vertex figureIrregular pentagon, edge lengths 1, 1, 1, 1, (5–1)/2
Great inverted snub icosidodecahedron vertfig.png
Measures (edge length 1)
Circumradius≈ 0.64502
Volume≈ 2.71387
Dihedral angles3–3: ≈ 89.78760°
 5/2–3: ≈ 21.61047°
Central density13
Number of external pieces780
Level of complexity65
Related polytopes
ArmyNon-uniform Snid
DualGreat inverted pentagonal hexecontahedron
ConjugatesSnub dodecahedron, Great snub icosidodecahedron, Great inverted retrosnub icosidodecahedron
Convex coreChiral order-6 truncated pentakis dodecahedron
Abstract & topological properties
Flag count600
Euler characteristic2
SymmetryH3+, order 60


The circumradius R ≈ 0.64502 of the great inverted snub icosidodecahedron with unit edge length is the second to smallest positive real root of:


Its volume V ≈ 2.71387 is given by the second to smallest positive real root of:


These same polynomials define the circumradii and volumes of the snub dodecahedron, the great snub icosidodecahedron, and the great inverted retrosnub icosidodecahedron.

Related polyhedraEdit

The great inverted disnub icosidodecahedron is a uniform polyhedron compound composed of the two opposite chiral forms of the great inverted snub icosidodecahedron.

o5/3o3o truncations
Name OBSA Schläfli symbol CD diagram Picture
Great stellated dodecahedron gissid {5/3,3} x5/3o3o (       )
Quasitruncated great stellated dodecahedron quit gissid t{5/3,3} x5/3x3o (       )
Great icosidodecahedron gid r{3,5/3} o5/3x3o (       )
Truncated great icosahedron tiggy t{3,5/3} o5/3x3x (       )
Great icosahedron gike {3,5/3} o5/3o3x (       )
Quasirhombicosidodecahedron qrid rr{3,5/3} x5/3o3x (       )
Great quasitruncated icosidodecahedron gaquatid tr{3,5/3} x5/3x3x (       )
Great inverted snub icosidodecahedron gisid sr{3,5/3} s5/3s3s (       )

External linksEdit