■DE群多面体の面数公式(その553)

 ワイソフ構成は3部よりなるが,1部2部はαと同じ,3部を局所幾何から求めればよい.

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[1]αnの局所幾何は(m+1,k+1)

  (1,2)

  (1,3,3)

  (1,4,6,4)

  (1,5,10,10,5)

  (1,6,15,20,15,6)

  (1,7,21,35,35,21,7)

  (1,8,28,56,70,56,28)

[2]βnの局所幾何は(m,k)2^m-k

  (1,2)

  (1,4,4)

  (1,6,12,8)

  (1,8,24,32,16)

  (1,10,40,80,80,32)

  (1,12,60,160,240,192,64)

  (1,14,84,280,560,672,448,128)

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[3]hγnの局所幾何は

  (1,1)

  (1,3,3)

  (1,6,12,8)

  (1,10,30,30,5+5)

  (1,15,60,80,30+15,6+6)

  (1,21,105,175,105+35,42+21,7+7)

  (1,28,168,336,280+70,168+56,56+28,8+8)

[4]Enの局所幾何は

  (1,3,1+2)

  (1,6,9,2+3

  (1,10,30,30,5+5)

  (1,16,80,160,120,10+16)

  (1,27,216,720,1080,216+432,72+27)

  (1,56,756,4032,10080,12096,6048,126+576)

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