# Quasitruncated great stellated dodecahedron

Quasitruncated great stellated dodecahedron
Rank3
TypeUniform
SpaceSpherical
Notation
Bowers style acronymQuit gissid
Coxeter diagramx5/3x3o ()
Elements
Faces20 triangles, 12 decagrams
Edges30+60
Vertices60
Vertex figureIsosceles triangle, edge lengths 1, (5–5)/2, (5–5)/2
Measures (edge length 1)
Circumradius${\displaystyle \sqrt{\frac{37-15\sqrt5}{8}} ≈ 0.65755}$
Volume${\displaystyle 5\frac{47\sqrt5-99}{12} ≈ 2.53966}$
Dihedral angles10/3–3: ${\displaystyle \arccos\left(\sqrt{\frac{5-2\sqrt5}{15}}\right) ≈ 79.18768^\circ}$
10/3–10/3: ${\displaystyle \arccos\left(\frac{\sqrt5}{5}\right) ≈ 63.43494^\circ}$
Central density13
Number of external pieces120
Level of complexity9
Related polytopes
ArmySemi-uniform Srid, edge lengths ${\displaystyle \sqrt5-2}$ (pentagons), ${\displaystyle \frac{3-\sqrt5}{2}}$ (triangles)
RegimentQuit gissid
DualGreat triakis icosahedron
ConjugateTruncated dodecahedron
Convex coreDodecahedron
Abstract & topological properties
Flag count360
Euler characteristic2
OrientableYes
Genus0
Properties
SymmetryH3, order 120
ConvexNo
NatureTame

The quasitruncated great stellated dodecahedron, or quit gissid, also called the great stellated truncated dodecahedron, is a uniform polyhedron. It consists of 20 triangles and 12 decagrams. Each vertex joins one triangle and two decagrams. As the name suggests, it can be obtained by quasitruncation of the great stellated dodecahedron.

## Vertex coordinates

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

• ${\displaystyle \left(0,\,±\frac12,\,±\frac{3\sqrt5-5}{4}\right),}$
• ${\displaystyle \left(±\frac12,\,±\frac{3-\sqrt5}{4},\,±\frac{3-\sqrt5}{2}\right),}$
• ${\displaystyle \left(±\frac{3-\sqrt5}{4},\,±\frac{\sqrt5-1}{2},\,±\frac{\sqrt5-2}{2}\right).}$

## Related polyhedra

o5/3o3o truncations
Name OBSA Schläfli symbol CD diagram Picture
Great stellated dodecahedron gissid {5/3,3} x5/3o3o ()
Quasitruncated great stellated dodecahedron quit gissid t{5/3,3} x5/3x3o ()
Great icosidodecahedron gid r{3,5/3} o5/3x3o ()
Truncated great icosahedron tiggy t{3,5/3} o5/3x3x ()
Great icosahedron gike {3,5/3} o5/3o3x ()
Quasirhombicosidodecahedron qrid rr{3,5/3} x5/3o3x ()
Great quasitruncated icosidodecahedron gaquatid tr{3,5/3} x5/3x3x ()
Great inverted snub icosidodecahedron gisid sr{3,5/3} s5/3s3s ()