Great icosicosidodecahedron

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Great icosicosidodecahedron
Great icosicosidodecahedron.png
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGiid
Coxeter diagramo3/2x3x5*a (CDel branch 11.pngCDel split2-5t.pngCDel node.png)
Elements
Faces20 triangles, 12 pentagons, 20 hexagons
Edges60+60
Vertices60
Vertex figureCrossed isosceles trapezoid, edge lengths 1, 3, (1+5)/2, 3
Great icosicosidodecahedron vertfig.png
Measures (edge length 1)
Circumradius
Volume
Dihedral angles5–6:
 3–6:
Central density6
Number of external pieces1232
Level of complexity75
Related polytopes
ArmyTid, edge length
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[edit | edit source]

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

Related polyhedra[edit | edit source]

o3/2o3o5*a truncations
Name OBSA CD diagram Picture
Great ditrigonary icosidodecahedron gidtid x3/2o3o5*a (CDel branch.pngCDel split2-5t.pngCDel node 1.png)
Great ditrigonal icosidodecahedron.png
(degenerate, 3ike+gad) x3/2x3o5*a (CDel branch 01r.pngCDel split2-5t.pngCDel node 1.png)
Icosahedron.png
(degenerate, double cover of gike) o3/2x3o5*a (CDel branch 01r.pngCDel split2-5t.pngCDel node.png)
Great icosahedron.png
Great icosicosidodecahedron giid o3/2x3x5*a (CDel branch 11.pngCDel split2-5t.pngCDel node.png)
Great icosicosidodecahedron.png
Great ditrigonary icosidodecahedron gidtid o3/2o3x5*a (CDel branch 10r.pngCDel split2-5t.pngCDel node.png)
Great ditrigonal icosidodecahedron.png
(degenerate, double cover of seihid) x3/2o3x5*a (CDel branch 10r.pngCDel split2-5t.pngCDel node 1.png)
Small icosihemidodecahedron.png
(degenerate, siddy+20(6/2)) x3/2x3x5*a (CDel branch 11.pngCDel split2-5t.pngCDel node 1.png)
(degenerate, 5ike+gad) s3/2s3s5*a
Icosahedron.png

External links[edit | edit source]