# Great ditrigonal dodecicosidodecahedron

(Redirected from Gidditdid)
Great ditrigonal dodecicosidodecahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGidditdid
Coxeter diagramx5/3x3o5*a (   )
Elements
Faces20 triangles, 12 pentagons, 12 decagrams
Edges60+60
Vertices60
Vertex figureIsosceles trapezoid, edge lengths 1, (5–5)/2, (1+5)/2, (5–5)/2 Measures (edge length 1)
Circumradius$\sqrt{\frac{17-3\sqrt5}{8}} ≈ 1.13423$ Volume$7\frac{15-\sqrt5}{6} ≈ 14.89125$ Dihedral angles3–10/3: $\arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°$ 5–10/3: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$ Central density4
Number of external pieces152
Level of complexity13
Related polytopes
ArmyTid, edge length $\frac{3-\sqrt5}{2}$ RegimentGidditdid
DualGreat ditrigonal dodecacronic hexecontahedron
ConjugateSmall ditrigonal dodecicosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count480
Euler characteristic-16
OrientableYes
Genus9
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great ditrigonal dodecicosidodecahedron, or gidditdid, is a uniform polyhedron. It consists of 20 triangles, 12 pentagons, and 12 decagrams. One triangle, one pentagon, and two decagrams join at each vertex.

## Vertex coordinates

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

• $\left(±\frac12,\,±\frac{\sqrt5-1}{2},\,±\frac{1+\sqrt5}{4}\right),$ • $\left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5}{2}\right),$ • $\left(±\frac12,\,±1,\,±\frac{3-\sqrt5}{4}\right).$ ## Related polyhedra

The great ditrigonal dodecicosidodecahedron is the colonel of a three-member regiment that also includes the great icosicosidodecahedron and the great dodecicosahedron.

o5/3o3o5*a truncations
Name OBSA CD diagram Picture
Ditrigonary dodecadodecahedron ditdid   Small complex icosidodecahedron (degenerate, ike+gad) cid   Great complex icosidodecahedron (degenerate, sissid+gike) gacid   Icosidodecadodecahedron ided   Small ditrigonal dodecicosidodecahedron sidditdid   Great ditrigonal dodecicosidodecahedron gidditdid   Icosidodecatruncated icosidodecahedron idtid   Snub icosidodecadodecahedron sided   