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]

Great dodecicosidodecahedron
TypeUniform star polyhedron
ElementsF = 44, E = 120
V = 60 (χ = 16)
Faces by sides20{3}+12{5/2}+12{10/3}
Wythoff symbol5/3
5/3 3/2 | 5/3
Symmetry groupIh, [5,3], *532
Index referencesU61, C77, W99
Dual polyhedronGreat dodecacronic hexecontahedron
Vertex figure
3.10/3.5/2.10/7
Bowers acronymGaddid
3D model of a great dodecicosidodecahedron.

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

References

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

See also

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