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Great dodecicosidodecahedron

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Great dodecicosidodecahedron
Type Uniform star polyhedron
Elements F = 44, E = 120
V = 60 (χ = −16)
Faces by sides 20{3}+12{5/2}+12{10/3}
Coxeter diagram
Wythoff symbol 5/2 3 | 5/3
5/3 3/2 | 5/3
Symmetry group Ih, [5,3], *532
Index references U61, C77, W99
Dual polyhedron Great dodecacronic hexecontahedron
Vertex figure
3.10/3.5/2.10/7
Bowers acronym Gaddid
3D model of a great dodecicosidodecahedron.

In geometry, the great dodecicosidodecahedron (or great dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U61. It has 44 faces (20 triangles, 12 pentagrams and 12 decagrams), 120 edges and 60 vertices.[1]

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It shares its vertex arrangement with the truncated great dodecahedron and the uniform compounds of 6 or 12 pentagonal prisms. It additionally shares its edge arrangement with the nonconvex great rhombicosidodecahedron (having the triangular and pentagrammic faces in common), and with the great rhombidodecahedron (having the decagrammic faces in common).


Nonconvex great rhombicosidodecahedron

Great dodecicosidodecahedron

Great rhombidodecahedron

Truncated great dodecahedron

Compound of six pentagonal prisms

Compound of twelve pentagonal prisms

See also

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References

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  1. ^ Maeder, Roman. "61: great dodecicosidodecahedron". MathConsult.
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