■DE群多面体の面数公式(その884)

 321の基本単体の頂点は,ρについて

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

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

P2(1,1/√3,0,0,0,0,0)

P3(1,1/√3,1/√6,0,0,0,0)

P4(1,1/√3,1/√6,1/√10,0,0,0)

P5(1,1/√3,1/√6,1/√10,1/√15,0,0)

P6(1,1/√3,1/√6,1/√10,1/√15,1/√21,0)

P7(1,1/√3,1/√6,1/√10,1/√15,1/√21,√(9/7))

  cosθ=21/{15+21}^1/2{21+7/9}^1/2

=21/6・3/14=3/4***

  cosθ=√(7/9)/{21+7/9}^1/2=√(7/9)√(9/196)=√(1/28)

σについて

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

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

P2(1,1/√3,0,0,0,0,0)

P3(1,1/√3,1/√6,0,0,0,0)

P4(1,1/√3,1/√6,1/√10,0,0,0)

P5(1,1/√3,1/√6,1/√10,1/√15,0,0)

P6(1,1/√3,1/√6,1/√10,1/√15,√(2/6),0)

P7(1,1/√3,1/√6,1/√10,1/√15,√(2/6),1)

  cosθ=15/{10+15}^1/2{15+3}^1/2=1/√2

  cosθ=3/{15+3}^1/2{3+1}^1/2=1/2√2***

  cosθ=1/{3+1}^1/2=1/2

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