Set of regular qgonal hosohedrons  

Example hexagonal hosohedron on a sphere 

Type  Regular polyhedron or spherical tiling 
Faces  q digons 
Edges  q 
Vertices  2 
Schläfli symbol  {2,q} 
Vertex configuration  2^{q} 
Coxeter–Dynkin diagram  
Wythoff symbol  q  2 2 
Symmetry group  Dihedral (D_{qh}) 
Dual polyhedron  dihedron 
In geometry, an ngonal hosohedron is a tessellation of lunes on a spherical surface, such that each lune shares the same two vertices. A regular ngonal hosohedron has Schläfli symbol {2, n}.
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For a regular polyhedron whose Schläfli symbol is {m, n}, the number of polygonal faces may be found by:
The platonic solids known to antiquity are the only integer solutions for m ≥ 3 and n ≥ 3. The restriction m ≥ 3 enforces that the polygonal faces must have at least three sides.
When considering polyhedrons as a spherical tiling, this restriction may be relaxed, since digons can be represented as spherical lunes, having nonzero area. Allowing m = 2 admits a new infinite class of regular polyhedrons, which are the hosohedrons. On a spherical surface, the polyhedron {2, n} is represented as n abutting lunes, with interior angles of 2π/n. All these lunes share two common vertices.
A regular trigonal hosohedron, represented as a tessellation of 3 spherical lunes on a sphere. 
A regular tetragonal hosohedron, represented as a tessellation of 4 spherical lunes on a sphere. 
The dual of the ngonal hosohedron {2, n} is the ngonal dihedron, {n, 2}. The polyhedron {2,2} is selfdual, and is both a hosohedron and a dihedron.
A hosohedron may be modified in the same manner as the other polyhedrons to produce a truncated variation. The truncated ngonal hosohedron is the ngonal prism.
Multidimensional analogues in general are called hosotopes, with Schläfli symbol {2,...,2,q}. A hosotope has two vertices.
The twodimensional hosotope {2} is a digon.
The prefix “hoso” was invented by H.S.M. Coxeter, and possibly derives from the English “hose”.

