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
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.