# Great snub dodecicosidodecahedral prism

Great snub dodecicosidodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymGisdiddip
Coxeter diagramx2s5/3s5/2s3*b ()
Elements
Cells20+60 triangular prisms, 24 pentagrammic prisms, 2 great snub dodecicosidodecahedra
Faces40+120 triangles, 60+60+60 squares, 48 pentagrams
Edges60+120+120+120
Vertices120
Vertex figureIrregular hexagonal pyramid, edge lengths 1, 1, 1, (5–1)/2, 1, (5–1)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\frac {\sqrt {3}}{2}}\approx 0.86603}$
Hypervolume${\displaystyle {\frac {5{\sqrt {2}}}{3}}\approx 2.35702}$
Dichoral anglesStip–4–trip #1: ${\displaystyle \arccos \left(-{\sqrt {\frac {5+2{\sqrt {5}}-4{\sqrt {5{\sqrt {5}}-10}}}{15}}}\right)\approx 125.77490^{\circ }}$
Trip–4–trip: ${\displaystyle \arccos \left(-{\frac {1}{3}}\right)\approx 109.47122^{\circ }}$
Gisdid–5/2–stip: 90°
Gisdid–3–trip: 90°
Stip–4–trip #2: ${\displaystyle \arccos \left({\sqrt {\frac {5+2{\sqrt {5}}+4{\sqrt {5{\sqrt {5}}-10}}}{15}}}\right)\approx 16.30368^{\circ }}$
Height1
Central density10
Number of external pieces602
Related polytopes
ArmySemi-uniform Sriddip
RegimentGisdiddip
DualGreat hexagonal hexecontahedral tegum
Abstract & topological properties
Euler characteristic–18
OrientableYes
Properties
SymmetryH3+×A1, order 120
ConvexNo
NatureTame

The great snub dodecicosidodecahedral prism or gisdiddip is a prismatic uniform polychoron that consists of 2 great snub dodecicosidodecahedra, 24 pentagrammic prisms (which form compounds in the same hyperplane), and 20+60 triangular prisms. Each vertex joins 1 great snub dodecicosidodecahedron,2 pentagrammic prisms, and 4 triangular prisms. As the name suggests, it is a prism based on the great snub dodecicosidodecahedron.

## Vertex coordinates

A great snub dodecicosidodecahedral prism of edge length 1 has vertex coordinates given by all even permutations of:

• ${\displaystyle \left(\pm {\sqrt {\frac {{\sqrt {5}}-1-2{\sqrt {{\sqrt {5}}-2}}}{2}}},\,\pm {\sqrt {\frac {3-{\sqrt {5}}-{\sqrt {10{\sqrt {5}}-22}}}{8}}},\,\pm {\sqrt {\frac {2+{\sqrt {2{\sqrt {5}}-2}}}{8}}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(0,\,\pm {\frac {\sqrt {3-{\sqrt {5}}}}{2}},\,\pm {\frac {\sqrt {{\sqrt {5}}-1}}{2}},\,\pm {\frac {1}{2}}\right),}$
• ${\displaystyle \left(\pm {\sqrt {\frac {3-{\sqrt {5}}+{\sqrt {10{\sqrt {5}}-22}}}{8}}},\,\pm {\sqrt {\frac {2-{\sqrt {2{\sqrt {5}}-2}}}{8}}},\,\pm {\sqrt {\frac {{\sqrt {5}}-1+2{\sqrt {{\sqrt {5}}-2}}}{8}}},\,\pm {\frac {1}{2}}\right).}$