# Quasitruncated great stellated dodecahedral prism

Quasitruncated great stellated dodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymQuit gissiddip
Coxeter diagramx x5/3x3o ()
Elements
Cells20 triangular prisms, 12 decagrammic prisms, 2 quasitruncated great stellated dodecahedra
Faces40 triangles, 30+60 squares, 24 decagrams
Edges60+60+120
Vertices120
Vertex figureSphenoid, edge lengths 1, 10–25/2, 10–25/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {39-15{\sqrt {5}}}{8}}}\approx 0.82606}$
Hypervolume${\displaystyle 5{\frac {47{\sqrt {5}}-99}{12}}\approx 2.53966}$
Dichoral anglesQuit gissid–10/3–stiddip: 90°
Quit gissid–3–trip: 90°
Trip–4–stiddip: ${\displaystyle \arccos \left({\sqrt {\frac {5-2{\sqrt {5}}}{15}}}\right)\approx 79.18769^{\circ }}$
Stiddip–4–stiddip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Height1
Central density13
Number of external pieces122
Related polytopes
ArmySemi-uniform Sriddip
RegimentQuit gissiddip
DualGreat triakis icosahedral tegum
ConjugateTruncated dodecahedral prism
Abstract & topological properties
Euler characteristic0
OrientableYes
Properties
SymmetryH3×A1, order 240
ConvexNo
NatureTame

The quasitruncated great stellated dodecahedral prism or quit gissiddip is a prismatic uniform polychoron that consists of 2 quasitruncated great stellated dodecahedra, 12 decagrammic prisms, and 20 triangular prisms. Each vertex joins 1 quasitruncated great stellated dodecahedron, 1 triangular prism, and 2 decagrammic prisms. As the name suggests, it is a prism based on the quasitruncated great stellated dodecahedron.

## Vertex coordinates

The vertices of a quasitruncated great stellated dodecahedral prism of edge length 1 are given by all even permutations of the first three coordinates of:

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