Great ditrigonal dodecicosidodecahedron

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Great ditrigonal dodecicosidodecahedron
Great ditrigonal dodecicosidodecahedron.png
Rank3
TypeUniform
SpaceSpherical
Bowers style acronymGidditdid
Info
Coxeter diagramx5/3x3o5*a
SymmetryH3, order 120
ArmyTid
RegimentGidditdid
Elements
Vertex figureIsosceles trapezoid, edge lengths 1, (5–5)/2, (1+5)/2, (5–5)/2
Faces20 triangles, 12 pentagons, 12 decagrams
Edges60+60
Vertices60
Measures (edge length 1)
Circumradius(17–35)/8 ≈ 1.13423
Volume7(15–5)/6 ≈ 14.89125
Dihedral angles3–10/3: acos(–(5+25)/15) ≈ 142.62263°
 5–10/3: acos(–5/5) ≈ 116.56505°
Central density4
Euler characteristic–16
Related polytopes
DualGreat ditrigonal dodecacronic hexecontahedron
ConjugateSmall ditrigonal dodecicosidodecahedron
Properties
ConvexNo
OrientableYes
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[edit | edit source]

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

  • (±1/2, ±(5–1)/4, ±(1+5)/2)
  • (0, ±(3–5)/4, ±5/2)
  • (±1/2, ±1, ±(3–5)/4)

Related polyhedra[edit | edit source]

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

External links[edit | edit source]