■基本単体の二面角(その154)

 E8について,・・・

===================================

【1】8次元の基本単体

α8:a1=1,a2=1/√3,a3=1/√6,a4=1/√10,a5=1/√15,a6=1/√21,a7=1/√28,a8=1/6

β8:a1=1,a2=1/√3,a3=1/√6,a4=1/√10,a5=1/√15,a6=1/√21,a7=1/√28,a8=1/2

 α8,β8の基本単体の底面同士を張り合わせると

  P0(0,0,0,0,0,0,0,0)

  P1(1,0,0,0,0,0,0,0)

  P2(1,1/√3,0,0,0,0,0,0)

  P3(1,1/√3,1/√6,0,0,0,0,0)

  P4(1,1/√3,1/√6,1/√10,0,0,0,0)

  P5(1,1/√3,1/√6,1/√10,1/√15,0,0,0)

  P6(1,1/√3,1/√6,1/√10,1/√15,1/√21,0,0)

  P7(1,1/√3,1/√6,1/√10,1/√15,1/√21,1/√28,0)

  P8(1,1/√3,1/√6,1/√10,1/√15,1/√21,1/√28,1/2)

  P8(1,1/√3,1/√6,1/√10,1/√15,1/√21,1/√28,1/6)

  P9(1,1/√3,1/√6,1/√10,1/√15,1/√21,1/√28,−1/2)

辺の長さは

1,√4/3,√3/2,√16/10,√5/3,√36/21,√147/84,√448/252

・・・・・・・・・・・・

1,√4/3,√3/2,√16/10,√5/3,√36/21,√147/84,1/2

===================================