# Quasitruncated small stellated dodecahedral prism

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

Quasitruncated small stellated dodecahedral prism
Rank4
TypeUniform
Notation
Bowers style acronymQuit sissiddip
Coxeter diagramx x5/3x5o ()
Elements
Cells12 pentagonal prisms, 12 decagrammic prisms, 2 quasitruncated small stellated dodecahedra
Faces30+60 squares, 24 pentagons, 24 decagrams
Edges60+60+120
Vertices120
Vertex figureSphenoid, edge lengths (1+5)/2, 5–5)/2, (5–5)/2 (base), 2 (legs)
Measures (edge length 1)
Circumradius${\displaystyle {\sqrt {\frac {19-5{\sqrt {5}}}{8}}}\approx 0.98867}$
Hypervolume${\displaystyle 11{\frac {3{\sqrt {5}}-5}{4}}\approx 4.69756}$
Dichoral anglesStiddip–4–stiddip: ${\displaystyle \arccos \left(-{\frac {\sqrt {5}}{5}}\right)\approx 116.56505^{\circ }}$
Quit sissid–5–pip: 90°
Quit sissid–10/3–stiddip: 90°
Stiddip–4–pip: ${\displaystyle \arccos \left({\frac {\sqrt {5}}{5}}\right)\approx 63.43495^{\circ }}$
Height1
Central density9
Number of external pieces110
Related polytopes
ArmySemi-uniform Sriddip
RegimentQuit sissiddip
DualGreat pentakis dodecahedral tegum
ConjugateTruncated great dodecahedral prism
Abstract & topological properties
Euler characteristic–8
OrientableYes
Properties
SymmetryH3×A1</ub>, order 240
ConvexNo
NatureTame

## Vertex coordinates

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

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