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A noble polyhedron is one which is isohedral (all faces the same) and isogonal (all vertices the same). They were first studied in any depth by Hess and Bruckner in late 19th century, and later by Grünbaum. ==Classes of noble polyhedra== There are four main classes of noble polyhedra: * The nine regular polyhedra are also noble. * Disphenoid tetrahedra. These and the Platonic solids are the only ''convex'' noble polyhedra. * Crown polyhedra or Stephanoids. An infinite series of toroids. * A variety of miscellaneous examples. It is not known whether there are finitely many, and if so how many might remain to be discovered. If we allow some of Grünbaum's stranger constructions as polyhedra, then we have two more infinite series of toroids: * Wreath polyhedra. These have triangular faces in coplanar pairs which share an edge. * V-faced polyhedra. These have vertices in coincident pairs, and degenerate faces. 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「Noble polyhedron」の詳細全文を読む スポンサード リンク
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