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polygonal dihedron
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polygonal dihedron

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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.

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 sections
Contents
  • 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.