Hosohedron

Set of regular n-gonal hosohedra
Set of regular n-gonal hosohedra
	Example regular hexagonal hosohedron on a sphere
Type	regular polyhedron or spherical tiling
Faces	n digons
Edges	n
Vertices	2
Euler char.	2
Vertex configuration	2n
Wythoff symbol	n \| 2 2
Schläfli symbol	{2,n}
Coxeter diagram
Symmetry group	Dnh ; [2,n] ; (*22n) ; order 4n
Rotation group	Dn ; [2,n]+ ; (22n) ; order 2n
Dual polyhedron	regular n-gonal dihedron

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 $.mw-parser-output .sfrac{white-space:nowrap}.mw-parser-output .sfrac.tion,.mw-parser-output .sfrac .tion{display:inline-block;vertical-align:-0.5em;font-size:85%;text-align:center}.mw-parser-output .sfrac .num{display:block;line-height:1em;margin:0.0em 0.1em;border-bottom:1px solid}.mw-parser-output .sfrac .den{display:block;line-height:1em;margin:0.1em 0.1em}.mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);clip-path:polygon(0px 0px,0px 0px,0px 0px);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px}⁠2π/n⁠$ radians ( $⁠ 360 / n ⁠$ degrees).^[1]^[2]

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

[1] Coxeter, Regular polytopes, p. 12

[2] Abstract Regular polytopes, p. 161

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