polygonal dihedron
Sign in to saveA dihedron (pl. dihedra) 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.
Key facts
- Polyhedron.name
- Set of regular n-gonal dihedra
- Polyhedron.image
- Hexagonal dihedron.svg
- Polyhedron.caption
- Example hexagonal dihedron on a sphere
- Polyhedron.type
- regular polyhedron or spherical tiling
- Polyhedron.faces
- 2 n-gons
- Polyhedron.edges
- n
- Polyhedron.vertices
- n
- Polyhedron.vertex_config
- n.n
- Polyhedron.schläfli
- {n,2}
- Polyhedron.wythoff
- 2 n 2
- Polyhedron.symmetry
- Dnh, [2,n], (*22n), order 4n
- Polyhedron.rotsymmetry
- Dn, [2,n]+, (22n), order 2n
- Polyhedron.dual
- regular n-gonal hosohedron
via Wikipedia infobox
Wikidata facts
- Image
- Pentagonal dihedron.png
Show 7 more facts
- has facet polytope
- polygon
- has vertex figure
- digon
- Schläfli symbol
- {n,2}
- dual to
- hosohedron
- studied by
- solid geometry
- Commons category
- Regular spherical dihedra
- maintained by WikiProject
- WikiProject Mathematics
Sources (1)
via Wikidata · CC0
~3 min read
Encyclopedic overview
7 sectionsContents
- As a flat-faced polyhedron
- As a tiling of the sphere
- Apeirogonal dihedron
- Ditopes
- See also
- References
- External links
{{Infobox polyhedron | name =Set of regular n-gonal dihedra | image =Hexagonal dihedron.svg | caption =Example hexagonal dihedron on a sphere | type =regular polyhedron or spherical tiling | euler = | faces =2 n-gons | edges =n | vertices =n | vertex_config =n.n | schläfli ={n,2} | wythoff =2 n 2 | coxeter = | symmetry =Dnh, [2,n], (*22n), order 4n | rotsymmetry =Dn, [2,n]+, (22n), order 2n | surface_area = | volume = | angle = | dual =regular n-gonal hosohedron | properties = | vertex_figure = | net =}} A dihedron (pl. dihedra) 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.
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.
Excerpted from Wikipedia’s “polygonal dihedron” article, available under the CC BY-SA 4.0 licence.