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In 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 , with each lune having internal angle 2π/''n'' radians (360/''n'' degrees).〔Coxeter, ''Regular polytopes'', p. 12〕〔Abstract Regular polytopes, p. 161〕 == Hosohedra as regular polyhedra == For a regular polyhedron whose Schläfli symbol is , 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 polyhedra as a spherical tiling, this restriction may be relaxed, since digons (2-gons) can be represented as spherical lunes, having non-zero area. Allowing ''m'' = 2 admits a new infinite class of regular polyhedra, which are the hosohedra. On a spherical surface, the polyhedron is represented as ''n'' abutting lunes, with interior angles of 2π/''n''. All these lunes share two common vertices. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Hosohedron」の詳細全文を読む スポンサード リンク
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