Great stellated truncated dodecahedron

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Great stellated truncated dodecahedron
Great stellated truncated dodecahedron.png
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 Great stellated truncated dodecahedron vertfig.png
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[edit]

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.png
Great stellated truncated dodecahedron
Small icosicosidodecahedron.png
Small icosicosidodecahedron
Small ditrigonal dodecicosidodecahedron.png
Small ditrigonal dodecicosidodecahedron
Small dodecicosahedron.png
Small dodecicosahedron

Cartesian coordinates[edit]

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).

See also[edit]

External links[edit]