# Great ditrigonary icosidodecahedral antiprism

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Great ditrigonary icosidodecahedral antiprism
Rank4
TypeUniform
SpaceSpherical
Notation
Bowers style acronymGidtidap
Coxeter diagram
Elements
Cells40 tetrahedra, 12 pentagonal antiprisms, 2 great ditrigonary icosidodecahedra
Faces40+120 triangles, 24 pentagons
Edges60+120
Vertices40
Vertex figureRetrotriangular cupola, edge lengths (1+5)/2 (3 base edges), 1 (remaining edges)
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{5+\sqrt5}{8}} ≈ 0.95106}$
Hypervolume0
Dichoral anglesGidtid–3–tet: ${\displaystyle \arccos\left(-\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 97.76124^\circ}$
Tet–3–pap: ${\displaystyle \arccos\left(\frac{\sqrt{7-3\sqrt5}}{4}\right) ≈ 82.23876^\circ}$
Gidtid–5–pap: ${\displaystyle \arccos\left(\frac{3-\sqrt5}{2}\right) ≈ 67.54448^\circ}$
Height${\displaystyle \sqrt{\frac{\sqrt5-1}{2}} ≈ 0.78615}$
Related polytopes
ArmySemi-uniform Dope
RegimentSidtidap
DualGreat triambic icosahedral antitegum
Abstract & topological properties
Euler characteristic–10
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The great ditrigonary icosidodecahedral antiprism or gidtidap, is a nonconvex uniform polychoron that consists of 2 great ditrigonary icosidodecahedra, 12 pentagonal antiprisms, and 40 tetrahedra. Each vertex joins 1 great ditrigonary icosidodecahedron, 3 pentagonal antiprisms, and 4 tetrahedra.

The pentagonal antiprism cells pass through the center of the polychoron, making it a hemipolychoron.

## Vertex coordinates

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