Hosohedron

Set of regular n-gonal hosohedra
Example regular hexagonal hosohedron on a sphere
Typeregular polyhedron or spherical tiling
Facesn digons
Edgesn
Vertices2
Euler char.2
Vertex configuration2n
Wythoff symboln | 2 2
Schläfli symbol{2,n}
Coxeter diagram
Symmetry groupDnh
[2,n]
(*22n)

order 4n
Rotation groupDn
[2,n]+
(22n)

order 2n
Dual polyhedronregular n-gonal dihedron
This beach ball would be a hosohedron with 6 spherical lune faces, if the 2 white caps on the ends were removed and the lunes extended to meet at the poles.

In spherical geometry, an n-gonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two polar opposite vertices.

A regular n-gonal hosohedron has Schläfli symbol {2,n}, with each spherical lune having internal angle 2π/nradians (360/n degrees).[1][2]

  1. ^ Coxeter, Regular polytopes, p. 12
  2. ^ Abstract Regular polytopes, p. 161