Great dodecicosidodecahedron

Great dodecicosidodecahedron
Great dodecicosidodecahedron.png
Type Uniform star polyhedron
Elements F = 44, E = 120
V = 60 (χ = −16)
Faces by sides 20{3}+12{5/2}+12{10/3}
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 Great dodecicosidodecahedron vertfig.png
3.10/3.5/2.10/7
Bowers acronym Gaddid

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]

3D model of a great dodecicosidodecahedron.

Related polyhedraEdit

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

ReferencesEdit

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

See alsoEdit

External linksEdit