■DE群多面体の面数公式(その885)

 421の基本単体の頂点は,ρについて

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)

P7(1,1/√3,1/√6,1/√10,1/√15,1/√21,1/√28,√(9/4))

  cosθ=28/{21+28}^1/2{28+4/9}^1/2=4/(16/3)=3/4***

  cosθ=√(4/9)/{28+4/9}^1/2=√(4/9)√(9/256)=√(1/64)=1/8

σについて

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,√(2/7),0)訂正した

P8(1,1/√3,1/√6,1/√10,1/√15,1/√21,√(2/7),√2)

  cosθ=21/{15+21}^1/2{21+7/2}^1/2=1/2√2***

  cosθ=7/2/{21+7/2}^1/2{7/2+1/2}^1/2=7/2・√2/7・1/2=1/2√2***これで整合した.

  cosθ=1/√2/{7/2+1/2}^1/2=1/2√2***

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