# Quasitruncated small stellated dodecahedron

Quasitruncated small stellated dodecahedron Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymQuit sissid
Coxeter diagramx5/3x5o (       )
Elements
Faces12 pentagons, 12 decagrams
Edges30+60
Vertices60
Vertex figureIsosceles triangle, edge lengths (1+5)/2, (5–5)/2, (5–5)/2 Measures (edge length 1)
Circumradius$\sqrt{\frac{17-5\sqrt5}{8}} ≈ 0.85291$ Volume$11\frac{3\sqrt5-5}{4} ≈ 4.69756$ Dihedral angles10/3–10/3: $\arccos\left(-\frac{\sqrt5}{5}\right) ≈ 116.56505°$ 5–10/3: $\arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43495°$ Central density9
Number of pieces132
Level of complexity11
Related polytopes
ArmySrid
RegimentQuit sissid
DualGreat pentakis dodecahedron
ConjugateTruncated great dodecahedron
Convex coreDodecahedron
Abstract properties
Euler characteristic–6
Topological properties
OrientableYes
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The quasitruncated small stellated dodecahedron, or quit sissid, also called the small stellated truncated dodecahedron, is a uniform polyhedron. It consists of 12 pentagons and 12 decagrams. Each vertex joins one pentagon and two decagrams. As the name suggests, it can be obtained by the quasitruncation of the small stellated dodecahedron.

## Vertex coordinates

A quasitruncated small stellated dodecahedron of edge length 1 has vertex coordinates given by all permutations of:

• $\left(±\frac{1+\sqrt5}{4},\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{4}\right),$ together with all even permutations of:

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

o5/3o5o truncations
Name OBSA Schläfli symbol CD diagram Picture
Small stellated dodecahedron sissid {5/3,5} x5/3o5o (       )
Quasitruncated small stellated dodecahedron quit sissid t{5/3,5} x5/3x5o (       )
Dodecadodecahedron did r{5,5/3} o5/3x5o (       )
Truncated great dodecahedron tigid t{5,5/3} o5/3x5x (       )
Great dodecahedron gad {5,5/3} o5/3o5x (       )
Complex ditrigonal rhombidodecadodecahedron (degenerate, ditdid+rhom) cadditradid rr{5,5/3} x5/3o5x (       )
Quasitruncated dodecadodecahedron quitdid tr{5,5/3} x5/3x5x (       )
Inverted snub dodecadodecahedron isdid sr{5,5/3} s5/3s5s (       )