Dihedron
A dihedron is a type of polyhedron, made of two polygon faces which share the same set of n edges. In three-dimensional Euclidean space, it is degenerate if its faces are flat, while in three-dimensional spherical space, a dihedron with flat faces can be thought of as a lens, an example of which is the fundamental domain of a lens space L(p,q). Dihedra have also been called bihedra, flat polyhedra, or doubly covered polygons.
| Set of regular n-gonal dihedra | |
|---|---|
Example hexagonal dihedron on a sphere | |
| Type | regular polyhedron or spherical tiling |
| Faces | 2 n-gons |
| Edges | n |
| Vertices | n |
| Vertex configuration | n.n |
| Wythoff symbol | 2 | n 2 |
| Schläfli symbol | {n,2} |
| Coxeter diagram | |
| Symmetry group | Dnh, [2,n], (*22n), order 4n |
| Rotation group | Dn, [2,n]+, (22n), order 2n |
| Dual polyhedron | regular n-gonal hosohedron |
As a spherical tiling, a dihedron can exist as nondegenerate form, with two n-sided faces covering the sphere, each face being a hemisphere, and vertices on a great circle. It is regular if the vertices are equally spaced.
The dual of an n-gonal dihedron is an n-gonal hosohedron, where n digon faces share two vertices.
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