Great snub dodecicosidodecahedron

In geometry, the great snub dodecicosidodecahedron (or great snub dodekicosidodecahedron) is a nonconvex uniform polyhedron, indexed as U64. It has 104 faces (80 triangles and 24 pentagrams), 180 edges, and 60 vertices.[1] It has Coxeter diagram, . It has the unusual feature that its 24 pentagram faces occur in 12 coplanar pairs.

Great snub dodecicosidodecahedron
TypeUniform star polyhedron
ElementsF = 104, E = 180
V = 60 (χ = −16)
Faces by sides(20+60){3}+(12+12){5/2}
Wythoff symbol| 5/3 5/2 3
Symmetry groupI, [5,3]+, 532
Index referencesU64, C80, W115
Dual polyhedronGreat hexagonal hexecontahedron
Vertex figure
3.3.3.5/2.3.5/3
Bowers acronymGisdid
3D model of a great snub dodecicosidodecahedron

It shares its vertices and edges, as well as 20 of its triangular faces and all its pentagrammic faces, with the great dirhombicosidodecahedron, (although the latter has 60 edges not contained in the great snub dodecicosidodecahedron). It shares its other 60 triangular faces (and its pentagrammic faces again) with the great disnub dirhombidodecahedron.

The edges and triangular faces also occur in the compound of twenty octahedra. In addition, 20 of the triangular faces occur in one enantiomer of the compound of twenty tetrahemihexahedra, and the other 60 triangular faces occur in the other enantiomer.


Convex hull
Great snub dodecicosidodecahedron
Great dirhombicosidodecahedron

Great disnub dirhombidodecahedron
Compound of twenty octahedra
Compound of twenty tetrahemihexahedra



Traditional filling
Modulo-2 filling
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See also

References
  1. Maeder, Roman. "64: great snub dodecicosidodecahedron". MathConsult.
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