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In graph theory, a nested triangles graph with ''n'' vertices is a planar graph formed from a sequence of ''n''/3 triangles, by connecting pairs of corresponding vertices on consecutive triangles in the sequence. It can also be formed geometrically, by gluing together ''n''/3 − 1 triangular prisms on their triangular faces. This graph, and graphs closely related to it, have been frequently used in graph drawing to prove lower bounds on the area requirements of various styles of drawings. ==Polyhedral representation== The nested triangles graph with two triangles is the graph of the triangular prism, and the nested triangles graph with three triangles is the graph of the triangular bifrustum. More generally, because the nested triangles graphs are planar and 3-vertex-connected, it follows from Steinitz's theorem that they all can be represented as convex polyhedra. An alternative geometric representation of these graphs may be given by gluing triangular prisms end-to-end on their triangular faces; the number of nested triangles is one more than the number of glued prisms. However, using right prisms, this gluing process will cause the rectangular faces of adjacent prisms to be coplanar, so the result will not be strictly convex. 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「Nested triangles graph」の詳細全文を読む スポンサード リンク
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