Dihedron
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| n-gonal dihedron | |
|---|---|
 | |
| Rank | 3 |
| Type | Regular |
| Space | Spherical |
| Notation | |
| Coxeter diagram |     (xno2o) |
| Schläfli symbol | {n,2} |
| Elements | |
| Faces | 2 n-gons |
| Edges | n |
| Vertices | n |
| Vertex figure | Digon |
| Measures (edge length 1) | |
| Dihedral angle | n-n: 0° |
| Central density | 1 |
| Related polytopes | |
| Army | n-gonal dihedron |
| Regiment | n-gonal dihedron |
| Dual | n-gonal hosohedron |
| Abstract properties | |
| Euler characteristic | 2 |
| Topological properties | |
| Surface | Sphere |
| Orientable | Yes |
| Genus | 0 |
| Properties | |
| Symmetry | I2(n)×A1, order 4n |
| Convex | Yes |
| Nature | Tame |
A dihedron is a polyhedron made of 2 faces which share all edges. It is degenerate if embedded in 3D Euclidean space, but it can be embedded in 3D spherical space. It can be thought of as a tiling of the sphere.
It is the three-dimensional case of a ditope.
Regular dihedra exist for all regular n-gons for n ≥ 2. The digonal dihedron, consisting of 2 digonal faces, is also the digonal hosohedron.
External links[edit | edit source]
- Wikipedia Contributors. "Dihedron".