|
In geometry, a polytope (a polygon, polyhedron or tiling, for example) is isogonal or vertex-transitive if, loosely speaking, all its vertices are the same. That implies that each vertex is surrounded by the same kinds of face in the same or reverse order, and with the same angles between corresponding faces. Technically, we say that for any two vertices there exists a symmetry of the polytope mapping the first isometrically onto the second. Other ways of saying this are that the group of automorphisms of the polytope is ''transitive on its vertices'', or that the vertices lie within a single ''symmetry orbit''. All vertices of a finite ''n''-dimensional isogonal figure exist on an (n-1)-sphere. The term isogonal has long been used for polyhedra. Vertex-transitive is a synonym borrowed from modern ideas such as symmetry groups and graph theory. The pseudorhombicuboctahedron — which is ''not'' isogonal — demonstrates that simply asserting that "all vertices look the same" is not as restrictive as the definition used here, which involves the group of isometries preserving the polyhedron or tiling. == Isogonal polygons and apeirogons== All regular polygons, apeirogons and regular star polygons are ''isogonal''. The dual of an isogonal polygon is an isotoxal polygon. Some even-sided polygons and apeirogons which alternate two edge lengths, for example rectangle, are ''isogonal''. All planar isogonal 2n-gons have dihedral symmetry (Dn, ''n''=2,3,...) with reflection lines across the mid-edge points. 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「Isogonal figure」の詳細全文を読む スポンサード リンク
|