Dihedron

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n -gonal dihedron
Rank3
Dimension2
TypeRegular
SpaceSpherical
Notation
Coxeter diagram (xn o2o)
Schläfli symbol{n,2}
Elements
Faces2 n -gons
Edgesn 
Verticesn 
Vertex figureDigon
Measures (edge length 1)
Dihedral anglen -n : 0°
Central density1
Related polytopes
Armyn -gonal dihedron
Regimentn -gonal dihedron
Dualn -gonal hosohedron
Petrie dual
  • n -gonal dihedron (for even n )
  • None (for odd n )
Abstract & topological properties
Flag count4n 
Euler characteristic0
OrientableYes
Genus0
SkeletonCn
Properties
SymmetryI2(n )×A1, order 4n 
ConvexYes
Net count1

A dihedron is a regular 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.

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