Great stellated truncated dodecahedron

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Short description: Polyhedron with 32 faces


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

File:Great stellated truncated dodecahedron.stl

In geometry, the great stellated truncated dodecahedron (or quasitruncated great stellated dodecahedron or great stellatruncated dodecahedron) is a nonconvex uniform polyhedron, indexed as U66. It has 32 faces (20 triangles and 12 decagrams), 90 edges, and 60 vertices.[1] It is given a Schläfli symbol t0,1{5/3,3}.

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,±φ,±[21φ])(±φ,±1φ,±2φ)(±1φ2,±1φ,±2)

where φ=1+52 is the golden ratio.

See also

References