# Great icosicosidodecahedron

(Redirected from Giid)
Great icosicosidodecahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGiid
Coxeter diagramo3/2x3x5*a (   )
Elements
Faces20 triangles, 12 pentagons, 20 hexagons
Edges60+60
Vertices60
Vertex figureCrossed isosceles trapezoid, edge lengths 1, 3, (1+5)/2, 3 Measures (edge length 1)
Circumradius$\sqrt{\frac{17-3\sqrt5}{8}} \approx 1.13423$ Volume$\frac{29\sqrt5-30}{3} \approx 11.61533$ Dihedral angles5–6: $\arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) \approx 79.18768^\circ$ 3–6: $\arccos\left(\frac{\sqrt5}{3}\right) \approx 41.81032^\circ$ Central density6
Number of external pieces1232
Level of complexity75
Related polytopes
ArmyTid, edge length $\frac{3-\sqrt5}{2}$ RegimentGidditdid
DualGreat icosacronic hexecontahedron
ConjugateSmall icosicosidodecahedron
Convex coreIcosahedron
Abstract & topological properties
Flag count480
Euler characteristic–8
OrientableYes
Genus5
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great icosicosidodecahedron, or giid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 20 hexagons. One triangle, one pentagon, and two hexagons join at each vertex.

It is a faceting of the great ditrigonal dodecicosidodecahedron, using its 12 pentagons and 20 triangles along with 20 additional hexagons.

A semi-uniform variant of this polyhedron can be constructed as a rectified great ditrigonary icosidodecahedron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the great ditrigonal dodecicosidodecahedron.

## Related polyhedra

o3/2o3o5*a truncations
Name OBSA CD diagram Picture
Great ditrigonary icosidodecahedron gidtid x3/2o3o5*a (   )
(degenerate, 3ike+gad) x3/2x3o5*a (   )
(degenerate, double cover of gike) o3/2x3o5*a (   )
Great icosicosidodecahedron giid o3/2x3x5*a (   )
Great ditrigonary icosidodecahedron gidtid o3/2o3x5*a (   )
(degenerate, double cover of seihid) x3/2o3x5*a (   )
(degenerate, siddy+20(6/2)) x3/2x3x5*a (   )