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Gosset graph : ウィキペディア英語版 | Gosset graph
The Gosset graph, named after Thorold Gosset, is a specific regular graph (1-skeleton of the 7-dimensional 321 polytope) with 56 vertices and valency 27.〔.〕 ==Construction== The Gosset graph can be explicitly constructed as follows: the 56 vertices are the vectors in R8, obtained by permuting the coordinates and possibly taking the opposite of the vector (3, 3, −1, −1, −1, −1, −1, −1). Two such vectors are adjacent when their inner product is 8. An alternative construction is based on the 8-vertex complete graph ''K''8. The vertices of the Gosset graph can be identified with two copies of the set of edges of ''K''8. Two vertices of the Gosset graph that come from the same copy are adjacent if they correspond to disjoint edges of ''K''8; two vertices that come from different copies are adjacent if they correspond to edges that share a single vertex.〔.〕
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「Gosset graph」の詳細全文を読む
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