Snub dodecadodecahedron
Snub dodecadodecahedron | |
---|---|
Type | Uniform star polyhedron |
Elements | F = 84, E = 150 V = 60 (χ = −6) |
Faces by sides | 60{3}+12{5}+12{5/2} |
Coxeter diagram | |
Wythoff symbol | | 2 5/2 5 |
Symmetry group | I, [5,3]+, 532 |
Index references | U40, C49, W111 |
Dual polyhedron | Medial pentagonal hexecontahedron |
Vertex figure | 3.3.5/2.3.5 |
Bowers acronym | Siddid |
In geometry, the snub dodecadodecahedron is a nonconvex uniform polyhedron, indexed as U40. It has 84 faces (60 triangles, 12 pentagons, and 12 pentagrams), 150 edges, and 60 vertices.[1] It is given a Schläfli symbol sr{5⁄2,5}, as a snub great dodecahedron.
Cartesian coordinates[edit]
Cartesian coordinates for the vertices of an inverted snub dodecadodecahedron are all the even permutations of
with an even number of plus signs, where
is the golden ratio, and α is the positive real root of
Taking the odd permutations of the above coordinates with an odd number of plus signs gives another form, the enantiomorph of the other one. Taking α to be the negative root gives the inverted snub dodecadodecahedron.
Related polyhedra[edit]
Medial pentagonal hexecontahedron[edit]
Medial pentagonal hexecontahedron | |
---|---|
Type | Star polyhedron |
Face | |
Elements | F = 60, E = 150 V = 84 (χ = −6) |
Symmetry group | I, [5,3]+, 532 |
Index references | DU40 |
dual polyhedron | Snub dodecadodecahedron |
The medial pentagonal hexecontahedron is a nonconvex isohedral polyhedron. It is the dual of the snub dodecadodecahedron. It has 60 intersecting irregular pentagonal faces.
See also[edit]
References[edit]
- ^ Maeder, Roman. "40: snub dodecadodecahedron". MathConsult.
- Wenninger, Magnus (1983), Dual Models, Cambridge University Press, doi:10.1017/CBO9780511569371, ISBN 978-0-521-54325-5, MR 0730208
External links[edit]
- Weisstein, Eric W. "Medial pentagonal hexecontahedron". MathWorld.
- Weisstein, Eric W. "Snub dodecadodecahedron". MathWorld.