Snub dodecahedron
In geometry, the snub dodecahedron, or snub icosidodecahedron, is an Archimedean solid, one of thirteen convex isogonal nonprismatic solids constructed by two or more types of regular polygon faces.
| Snub dodecahedron | |
|---|---|
(Click here for rotating model) | |
| Type | Archimedean solid Uniform polyhedron |
| Elements | F = 92, E = 150, V = 60 (χ = 2) |
| Faces by sides | (20+60){3}+12{5} |
| Conway notation | sD |
| Schläfli symbols | sr{5,3} or |
| ht0,1,2{5,3} | |
| Wythoff symbol | | 2 3 5 |
| Coxeter diagram | |
| Symmetry group | I, 1/2H3, [5,3]+, (532), order 60 |
| Rotation group | I, [5,3]+, (532), order 60 |
| Dihedral angle | 3-3: 164°10′31″ (164.18°) 3-5: 152°55′53″ (152.93°) |
| References | U29, C32, W18 |
| Properties | Semiregular convex chiral |
Colored faces |
3.3.3.3.5 (Vertex figure) |
Pentagonal hexecontahedron (dual polyhedron) |
Net |
The snub dodecahedron has 92 faces (the most of the 13 Archimedean solids): 12 are pentagons and the other 80 are equilateral triangles. It also has 150 edges, and 60 vertices.
It has two distinct forms, which are mirror images (or "enantiomorphs") of each other. The union of both forms is a compound of two snub dodecahedra, and the convex hull of both forms is a truncated icosidodecahedron.
Kepler first named it in Latin as dodecahedron simum in 1619 in his Harmonices Mundi. H. S. M. Coxeter, noting it could be derived equally from either the dodecahedron or the icosahedron, called it snub icosidodecahedron, with a vertical extended Schläfli symbol and flat Schläfli symbol sr{5,3}.
