■n次元の立方体と直角三角錐(その157)

 ファセット数公式の正当性が実証されたが,辺数・頂点数公式については

         [0,1,0,0]

 (1,0,0)→[1,0,1,0]

         [2,0,0,1]

も加えてみても見当がつかない.やむなく4次元正16胞体に移ることにした.

  f0=8,f1=24,f2=32,f3=16

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[1](0,1,0,0)→f=(24,96,96,24)

  [0,0,1,0,0],[0,1,0,0,1],[0,3,0,0,0]

  [1,0,0,3,0],[1,1,1,2,0],[1,0,0,2,2],[1,2,0,2,1],[1,4,0,2,0],[1,5,1,1,0],[1,4,0,1,2],[1,6,0,1,1],[1,8,0,1,0],[1,0,4,0,0],[1,1,3,0,1],[1,3,3,0,0],[1,0,2,0,2],[1,2,2,0,2],[1,4,2,0,1],[1,6,2,0,0],[1,5,1,0,2],[1,7,1,0,1],[1,9,1,0,0],[1,8,0,0,2],[1,10,0,0,1],[1,12,0,0,0]

[2](0,0,1,0)→f=(32,96,88,24)

  [0,0,0,1,0],[0,1,1,0,0],[0,0,0,0,2],[0,2,0,0,1],[0,4,0,0,0]

  [2,0,1,2,0],[2,1,0,2,1],[2,3,0,2,0],[2,1,2,1,0],[2,0,1,1,2],[2,2,1,1,1],[2,4,1,1,0],

[2,1,0,1,3],[2,3,0,1,2],[2,5,0,1,1],[2,7,0,1,0],[2,0,3,0,1],[2,2,3,0,01,[2,1,2,0,1],[2,3,2,0,0],[2,0,1,0,41,[2,2,1,0,31,[2,4,1,0,2],[2,6,1,0,1],[2,8,1,0,0],[2,1,0,0,5],[2,3,0,0,4],[2,5,1,0,3],[2,7,0,0,2],[2,9,0,0,1],[2,11,0,0,0]

[3](0,0,0,1)→f=(16,32,24,8)

  [0,0,0,0,1]

  [1,0,0,1,0]

  [2,0,1,0,0]

  [3,1,0,0,0]

[4](1,1,0,0)→f=(48,120,96,24)

  [0,0,0,1,1],[0,2,0,1,0],[0,1,1,0,1],[0,3,1,0,0],[0,0,0,0,3],[0,2,0,0,2],[0,4,0,0,1],[0,6,0,0,0]

  [1,0,1,3,0],[1,1,0,3,1],[1,3,0,3,0],[1,1,2,2,0],[1,2,1,2,1],[1,4,1,2,0],[1,1,0,2,3],[1,3,0,2,2],[1,5,0,2,1],[1,7,0,2,0],[1,0,3,1,1],[1,2,3,1,0],[1,1,2,1,2],[1,3,2,1,1],[1,5,2,1,0],[1,0,1,1,4],[1,2,1,1,3],[1,4,1,1,2],[1,6,1,1,1],[1,8,1,1,0],[1,7,0,1,2],[1,9,0,1,1],[1,11,0,1,0],[1,0,5,0,0],[1,1,4,0,1],[1,3,4,0,0],[1,0,3,0,3],[1,2,3,0,2],[1,4,3,0,1],[1,6,3,0,0],[1,1,2,0,4],[1,3,2,0,3],[1,5,2,0,2],[1,7,2,0,1],[1,9,2,0,0],[1,0,1,0,6],[1,2,1,0,5],[1,4,1,0,4],[1,6,1,0,3],[1,8,1,0,2],[1,10,1,0,1],[1,12,1,0,0],[1,11,0,0,2],[1,13,0,0,1],[1,15,0,0,0]

[5](1,0,1,0)→f=(96,288,240,48)

  [1,0,0,9,0],[1,1,1,8,0],[1,0,0,8,2],[1,2,0,8,1],[1,4,0,8,0],[1,0,2,7,1],[1,2,2,7,0],[1,1,1,7,2],[1,3,1,7,1],[1,5,1,7,0],[1,0,0,7,4],[1,2,0,7,3],[1,4,0,7,2],[1,6,0,7,1],[1,8,0,7,0],[1,0,4,6,0],[1,1,3,6,1],[1,3,3,6,0],[1,0,2,6,3],[1,2,2,6,2],[1,4,2,6,1],[1,6,2,6,0],[1,1,1,6,4],[1,3,1,6,3],[1,5,1,6,2],[1,7,1,6,1],[1,9,1,6,0],[1,0,0,6,6],[1,2,0,6,5],[1,4,0,6,4],[1,6,0,6,3],[1,8,0,6,2],[1,10,0,6,1],[1,12,0,6,0],[1,1,5,5,0],[1,2,4,5,1],[1,4,4,5,0],[1,3,3,5,2],[1,5,3,5,1],[1,7,3,5,0],[1,0,2,5,5],[1,2,2,5,4],[1,4,2,5,3],[1,6,2,5,2],[1,8,2,5,1],[1,10,2,5,0],[1,1,1,5,6],[1,3,1,5,5],[1,5,1,5,4],[1,7,1,5,3],[1,9,1,5,2],[1,11,1,5,1],[1,13,1,5,0],[1,0,0,5,8],[1,2,0,5,7],[1,4,0,5,6],[1,6,0,5,5],[1,8,0,5,4],[1,10,0,5,3],[1,12,0,5,2],[1,14,0,5,1],[1,16,0,5,0],[1,2,0,5,7],[1,4,0,5,6],[1,6,0,5,5],[1,8,0,5,4],[1,10,0,5,3],[1,12,0,5,2],[1,14,0,5,1],[1,16,0,5,0],[1,0,6,4,1],[1,2,6,4,0],[1,3,5,4,1],[1,5,5,4,0],[1,0,4,4,4],[1,2,4,4,3],[1,4,4,4,2],[1,6,4,4,1],[1,8,4,4,0],[1,1,3,4,5],[1,3,3,4,4],[1,5,3,4,3],[1,7,3,4,2],[1,9,3,4,1],[1,11,3,4,0],[1,0,2,4,7],[1,2,2,4,6],[1,4,2,4,5],[1,6,2,4,4],[1,8,2,4,3],[1,10,2,4,2],[1,12,2,4,1],[1,14,2,4,0],[1,1,1,4,8],[1,3,1,4,7],[1,5,1,4,6],[1,7,1,4,5],[1,9,1,4,4],[1,11,1,4,3],[1,13,1,4,2],[1,15,1,4,1],[1,17,1,4,0],[1,0,0,4,10],[1,2,0,4,9],[1,4,0,4,8],[1,6,0,4,7],[1,8,0,4,6],[1,10,0,4,5],[1,12,0,4,4],[1,14,0,4,3],[1,16,0,4,2],[1,18,0,4,1],[1,20,0,4,0],[1,0,8,3,0],[1,1,7,3,1],[1,3,7,3,0],[1,0,8,3,0],[1,1,7,3,1],[1,3,7,3,0],[1,0,6,3,3],[1,2,6,3,2],[1,4,6,3,1],[1,6,6,3,0],[1,1,5,3,4],[1,3,5,3,3],[1,5,5,3,2],[1,7,5,3,1],[1,9,5,3,0],[1,0,4,3,6],[1,2,4,3,5],[1,4,4,3,4],[1,6,4,3,3],[1,8,4,3,2],[1,10,4,3,1],[1,12,4,3,0],[1,1,3,3,7],[1,3,3,3,6],[1,5,3,3,5],[1,7,3,3,4],[1,9,3,3,3],[1,11,3,3,2],[1,13,3,3,1],[1,15,3,3,0],[1,0,2,3,9],[1,1,2,3,8],[1,3,2,3,7],[1,5,2,3,6],[1,7,2,3,5],[1,9,2,3,4],[1,11,2,3,3],[1,13,2,3,2],[1,15,2,3,1],[1,17,2,3,0],[1,1,1,3,10],[1,3,1,3,9],[1,5,1,3,8],[1,7,1,3,7],[1,9,1,3,6],[1,11,1,3,5],[1,13,1,3,4],[1,15,1,3,3],[1,17,1,3,2],[1,19,1,3,1][1,21,1,3,0],[1,0,0,3,12],[1,2,0,3,11],[1,4,0,3,10],[1,6,0,3,9],[1,8,0,3,8],[1,10,0,3,7],[1,12,0,3,6],[1,14,0,3,5],[1,16,0,3,4],[1,18,0,3,3],[1,20,0,3,2],[1,22,0,3,1],[1,24,0,3,0],[1,1,9,2,0],[1,2,8,2,1],[1,4,8,2,0],[1,5,7,2,1],[1,7,7,2,0],[1,8,6,2,1],[1,10,6,2,0],[1,11,5,2,1],[1,13,5,2,0],[1,14,4,2,1],[1,16,4,2,0],[1,17,3,2,1],[1,19,3,2,0],[1,20,2,2,1],[1,22,2,2,0],[1,23,1,2,1],[1,25,1,2,0],[1,26,0,2,1],[1,28,0,2,0],[1,0,10,1,1],[1,2,10,1,0],[1,3,9,1,1],[1,5,9,1,0],,[1,6,8,1,1],[1,8,8,1,0],[1,9,7,1,1],[1,11,7,1,0],[1,12,6,1,1],[1,14,6,1,0],[1,15,5,1,1],[1,17,5,1,0],[1,18,4,1,1],[1,20,4,1,0],[1,21,3,1,1],[1,23,3,1,0],[1,24,2,1,1],[1,26,2,1,0],[1,27,1,1,1],[1,29,1,1,0],[1,30,0,1,1],[1,32,0,1,0],[1,0,12,0,0],[1,1,11,0,1],[1,3,11,0,0],[1,4,10,0,1],[1,6,10,0,0],[1,7,9,0,1],,[1,9,9,0,0],[1,10,8,0,1],[1,12,8,0,0],[1,13,7,0,1],[1,15,7,0,0],[1,16,6,0,1],[1,18,6,0,0],[1,19,5,0,1],[1,21,5,0,0],[1,22,4,0,1],[1,24,4,0,0],[1,25,3,0,1],[1,27,3,0,0],[1,28,2,0,1],[1,30,2,0,0],[1,31,1,0,1],[1,33,1,0,0],[1,34,0,0,1],[1,36,0,0,0]

  [2,0,0,7,1],[2,2,0,7,0],[2,0,2,6,0],[2,1,1,6,1],[2,3,1,6,0],[2,0,0,6,3],[2,2,0,6,2],[2,4,0,6,1],[2,6,0,6,0],[2,1,3,5,0],[2,2,2,5,1],[2,4,2,5,0],[2,1,1,5,3],[2,3,1,5,2],[2,5,1,5,1],[2,7,1,5,0],[2,0,0,5,5],[2,2,0,5,4],[2,4,0,5,3],[2,6,0,5,2],[2,8,0,5,1],[2,10,0,5,0],[2,0,4,4,1],[2,2,4,4,0],[2,3,3,4,1],[2,5,3,4,0],[2,6,2,4,1],[2,8,2,4,0],[2,9,1,4,1],[2,11,1,4,0],[2,12,0,4,1],[2,14,0,4,0],[2,0,6,3,0],[2,1,5,3,1],[2,3,5,3,0],[2,4,4,3,1],[2,6,4,3,0],[2,7,3,3,1],[2,9,3,3,0],[2,10,2,3,1],[2,12,2,3,0],[2,13,1,3,1],[2,15,1,3,0],[2,0,0,3,9],[2,2,0,3,8],[2,4,0,3,7],[2,6,0,3,6],[2,8,0,3,5],[2,10,0,3,4],[2,12,0,3,3],[2,14,0,3,2],[2,16,0,3,1],[2,18,0,3,0],[2,1,7,2,0],[2,2,6,2,1],[2,4,6,2,0],[2,1,5,2,3],[2,3,5,2,2],[2,5,5,2,1],[2,7,5,2,0],[2,0,4,2,5],[2,2,4,2,4],[2,4,4,2,3],[2,6,4,2,2],[2,8,4,2,1],[2,10,4,2,0],[2,1,3,2,6],[2,3,3,2,5],[2,5,3,2,4],[2,7,3,2,3],[2,9,3,2,2],[2,11,3,2,1],[2,13,3,2,0],[2,0,2,2,8],[2,2,2,2,7],[2,4,2,2,6],[2,6,2,2,5],[2,8,2,2,4],[2,10,2,2,3],[2,12,2,2,2],[2,14,2,2,1],[2,16,2,2,0],[2,1,1,2,9],[2,3,1,2,8],[2,5,1,2,7],[2,7,1,2,6],[2,9,1,2,5],[2,11,1,2,4],[2,13,1,2,3],[2,15,1,2,2],[2,17,1,2,1],[2,19,1,2,0],[2,0,0,2,11],[2,2,0,2,10],[2,4,0,2,9],[2,6,0,2,8],[2,8,0,2,7],[2,10,0,2,6],[2,12,0,2,5],[2,14,0,2,4],[2,16,0,2,3],[2,18,0,2,2],[2,20,0,2,1],[2,22,0,2,0],[2,0,8,1,1],[2,2,8,1,0],[2,3,7,1,1],[2,5,7,1,0],[2,6,6,1,1],[2,8,6,1,0],[2,9,5,1,1],[2,11,5,1,0],[2,12,4,1,1],[2,14,4,1,0],[2,15,3,1,1],[2,17,3,1,0],[2,18,2,1,1],[2,20,2,1,0],[2,21,1,1,1],[2,23,1,1,0],[2,24,0,1,1],[2,26,0,1,0],[2,0,10,0,0],[2,1,9,0,1],[2,2,9,0,0],[2,3,8,0,1],[2,5,8,0,0],[2,6,7,0,1],[2,8,7,0,0],[2,9,6,0,1],[2,11,6,0,0],[2,12,5,0,1],[2,14,5,0,0],[2,15,4,0,1],[2,17,4,0,0],[2,18,3,0,1],[2,20,3,0,0],[2,21,2,0,1],[2,23,2,0,0],[2,24,1,0,1],[2,26,1,0,0],[2,0,0,0,15],[2,2,0,0,14],[2,4,0,0,13],[2,6,0,0,12],[2,8,0,0,11],[2,10,0,0,10],[2,12,0,0,9],[2,14,0,0,8],[2,16,0,0,7],[2,18,0,0,6],[2,20,0,0,5],[2,22,0,0,4],[2,24,0,0,3],[2,26,0,0,2],[2,28,0,0,1],[2,30,0,0,0]

 長くなったので,ここで中断.

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