■基本単体の二面角(その154)
E8について,・・・
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【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
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