# Great stellated truncated dodecahedron

Great stellated truncated dodecahedron
Type Uniform star polyhedron
Elements F = 32, E = 90
V = 60 (χ = 2)
Faces by sides 20{3}+12{10/3}
Wythoff symbol 2 3 | 5/3
Symmetry group Ih, [5,3], *532
Index references U66, C83, W104
Dual polyhedron Great triakis icosahedron
Vertex figure
3.10/3.10/3
Bowers acronym Quit Gissid

In geometry, the great stellated truncated dodecahedron or quasitruncated great stellated dodecahedron is a nonconvex uniform polyhedron, indexed as U66. It is given a Schläfli symbol t0,1{5/3,3}.

## Related polyhedra

It shares its vertex arrangement with three other uniform polyhedra: the small icosicosidodecahedron, the small ditrigonal dodecicosidodecahedron, and the small dodecicosahedron:

 Great stellated truncated dodecahedron Small icosicosidodecahedron Small ditrigonal dodecicosidodecahedron Small dodecicosahedron

## Cartesian coordinates

Cartesian coordinates for the vertices of a great stellated truncated dodecahedron are all the even permutations of

(0, ±τ, ±(2−1/τ))
(±τ, ±1/τ, ±2/τ)
(±1/τ2, ±1/τ, ±2)

where τ = (1+√5)/2 is the golden ratio (sometimes written φ).