# Great dodecicosidodecahedral prism

Great dodecicosidodecahedral prism
Rank4
TypeUniform
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${\displaystyle {\frac {{\sqrt {10}}-{\sqrt {2}}}{2}}\approx 0.87403}$
Hypervolume${\displaystyle 2{\frac {45-17{\sqrt {5}}}{3}}\approx 4.6790}$
Dichoral anglesStip–4–stiddip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Trip–4–stiddip: ${\displaystyle \arccos \left(-{\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 100.81232^{\circ }}$
Height1
Central density10
Number of external pieces182
Related polytopes
ArmySemi-uniform Tipe
DualGreat dodecacronic hexecontahedral tegum
ConjugateSmall dodecicosidodecahedral prism
Abstract & topological properties
Euler characteristic–18
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:

• ${\displaystyle \left(\pm {\frac {1}{2}},\,\pm {\frac {1}{2}},\,\pm {\frac {{\sqrt {5}}-2}{2}},\,\pm {\frac {1}{2}}\right),}$

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

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