# Great dodecicosidodecahedral prism

Great dodecicosidodecahedral prism
Rank4
TypeUniform
SpaceSpherical
Notation
Coxeter diagramx x5/3x5/2o3*b ()
Elements
Cells20 triangular prisms, 12 pentagrammic prisms, 12 decagrammic prisms, 2 great dodecicosidodecahedra
Faces40 triangles, 60+60 squares, 24 pentagrams, 24 decagrams
Edges60+120+120
Vertices120
Vertex figureIsosceles trapezoidal pyramid, edge lengths 1, (5–5)/2, (5–1)/2, (5–5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle \frac{\sqrt{10}-\sqrt2}{2} ≈ 0.87403}$
Hypervolume${\displaystyle 2\frac{45-17\sqrt5}{3} ≈ 4.6790}$
Dichoral anglesStip–4–stiddip: ${\displaystyle \arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°}$
Trip–4–stiddip: ${\displaystyle \arccos\left(-\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 100.81232°}$
Height1
Central density10
Number of pieces182
Related polytopes
ArmySemi-uniform Tipe
DualGreat dodecacronic hexecontahedral tegum
ConjugateSmall dodecicosidodecahedral prism
Abstract properties
Euler characteristic–18
Topological properties
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The great dodecicosidodecahedral prism or gaddiddip is a prismatic uniform polychoron that consists of 2 great dodecicosidodecahedra, 12 pentagrammic prisms, 20 triangular prisms, and 12 decagrammic prisms. Each vertex joins 1 great dodecicosidodecahedron, 1 pentagrammic prism, 1 triangular prism, and 2 decagrammic prisms. As the name suggests, it is a prism based on the great dodecicosidodecahedron.

The great dodecicosidodecahedral prism can be vertex-inscribed into the grand ditetrahedronary hexacosidishecatonicosachoron.

## Vertex coordinates

The vertices of a great dodecicosidodecahedral prism of edge length 1 are given by all permutations of the first three coordinates of:

• ${\displaystyle \left(±\frac12,\,±\frac12,\,±\frac{\sqrt5-2}{2},\,±\frac12\right),}$

along with all even permutations of the first three coordinates of:

• ${\displaystyle \left(0,\,±\frac{3-\sqrt5}{4},\,±\frac{5-\sqrt5}{4},\,±\frac12\right),}$
• ${\displaystyle \left(±\frac{\sqrt5-1}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{3-\sqrt5}{4},\,±\frac12\right).}$