# Great ditrigonary icosidodecahedron

Great ditrigonary icosidodecahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGidtid
Coxeter diagramx3/2o3o5*a ()
Elements
Faces20 triangles, 12 pentagons
Edges60
Vertices20
Vertex figureTripod, edge lengths 1 and (1+5)/2
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt3}{2} ≈ 0.86603}$
Volume${\displaystyle \frac{4\sqrt5}{3} ≈ 2.98142}$
Dihedral angle${\displaystyle \arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768^\circ}$
Central density6
Number of external pieces300
Level of complexity15
Related polytopes
ArmyDoe, edge length ${\displaystyle \frac{\sqrt5-1}{2}}$
RegimentSidtid
DualGreat triambic icosahedron
ConjugateSmall ditrigonary icosidodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count240
Euler characteristic–8
OrientableYes
Genus5
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The great ditrigonary icosidodecahedron or gidtid is a quasiregular uniform polyhedron. It consists of 20 equilateral triangles and 12 pentagons, with three of each joining at a vertex.

It is a faceting of the small ditrigonary icosidodecahedron, using its 20 triangles along with 12 additional pentagons.

It can be constructed as a holosnub great stellated dodecahedron.

This polyhedron is the vertex figure of the great ditrigonary hexacosihecatonicosachoron.

## Vertex coordinates

Its vertices are the same as those of its regiment colonel, the small ditrigonary icosidodecahedron.

## Representations

A great ditrigonary icosidodecahedron has the following Coxeter diagrams:

• x3/2o3o5*a
• ß5/2o3o (, as holosnub)

## Related polyhedra

o3/2o3o5*a truncations
Name OBSA CD diagram Picture
Great ditrigonary icosidodecahedron gidtid x3/2o3o5*a ()