Great ditrigonal dodecicosidodecahedron

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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${\displaystyle \sqrt{\frac{17-3\sqrt5}{8}} ≈ 1.13423}$
Volume${\displaystyle 7\frac{15-\sqrt5}{6} ≈ 14.89125}$
Dihedral angles3–10/3: ${\displaystyle \arccos\left(-\sqrt{\frac{5+2\sqrt5}{15}}\right) ≈ 142.62263°}$
5–10/3: ${\displaystyle \arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°}$
Central density4
Number of external pieces152
Level of complexity13
Related polytopes
ArmyTid, edge length ${\displaystyle \frac{3-\sqrt5}{2}}$
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:

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

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