Great dodecicosidodecahedron

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Great dodecicosidodecahedron
Rank3
TypeUniform
Notation
Bowers style acronymGaddid
Coxeter diagramx5/3x5/2o3*a ()
Elements
Faces20 triangles, 12 pentagrams, 12 decagrams
Edges60+60
Vertices60
Vertex figureIsosceles trapezoid, edge lengths 1, (5–5)/2, (5–1)/2, (5–5)/2
Measures (edge length 1)
Circumradius
Volume
Dihedral angles5/2–10/3:
 3–10/3:
Central density10
Number of external pieces180
Level of complexity13
Related polytopes
ArmySemi-uniform Ti, edge lengths (pentagons), (between ditrigons)
RegimentGaddid
DualGreat dodecacronic hexecontahedron
ConjugateSmall dodecicosidodecahedron
Convex coreTruncated dodecahedron
Abstract & topological properties
Flag count480
Euler characteristic–16
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great dodecicosidodecahedron, or gaddid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagrams, and 12 decagrams. One triangle, one pentagram, and two decagrams join at each vertex.

Vertex coordinates[edit | edit source]

A great dodecicosidodecahedron of edge length 1 has vertex coordinates given by all permutations of

along with all even permutations of

Related polyhedra[edit | edit source]

The great dodecicosidodecahedron is the colonel of a three-member regiment that also includes the quasirhombicosidodecahedron and the great rhombidodecahedron.

o5/3o5/2o3*a truncations
Name OBSA CD diagram Picture
Great complex icosidodecahedron (degenerate, sissid+gike) gacid x5/3o5/2o3*a ()
Great dodecicosidodecahedron gaddid x5/3x5/2o3*a ()
(degenerate, double cover of gissid) o5/3x5/2o3*a ()
(degenerate, ditdid+gidtid) o5/3x5/2x3*a ()
Great complex icosidodecahedron (degenerate, sissid+gike) gacid o5/3o5/2x3*a ()
(degenerate, double cover of sidhei) x5/3o5/2x3*a ()
(degenerate, giddy+12(10/2)) x5/3x5/2x3*a ()
Great snub dodecicosidodecahedron gisdid s5/3s5/2s2*a ()

External links[edit | edit source]