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|- |bgcolor=#e7dcc3|Symmetry group||L2(19) (order 3420) |- |bgcolor=#e7dcc3|Dual||self-dual |- |bgcolor=#e7dcc3|Properties||Regular |} In mathematics, the 57-cell (pentacontakaiheptachoron) is a self-dual abstract regular 4-polytope (four-dimensional polytope). Its 57 cells are hemi-dodecahedra. It also has 57 vertices, 171 edges and 171 two-dimensional faces. Its symmetry group is the projective special linear group L2(19), so it has 3420 symmetries. It has Schläfli symbol with 5 hemi-dodecahedral cells around each edge. It was discovered by . == Perkel graph == The vertices and edges form the Perkel graph, the unique distance-regular graph with intersection array , discovered by . 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「57-cell」の詳細全文を読む スポンサード リンク
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