■DE群多面体の面数公式(その850)
cosθ=bn/{bn-1^2+bn^2}^1/2
を計算してみたい.
===================================
221の基本単体の頂点は,ρについて
P0(0,0,0,0,0,0)
P1(1,0,0,0,0,0)
P2(1,1/√3,0,0,0,0)
P3(1,1/√3,1/√6,0,0,0)
P4(1,1/√3,1/√6,1/√10,0,0)
P5(1,1/√3,1/√6,1/√10,1/√15,0)
P6(1,1/√3,1/√6,1/√10,1/√15,1)
cosθ=1/{16}^1/2=1/4
σについて
P0(0,0,0,0,0,0)
P1(1,0,0,0,0,0)
P2(1,1/√3,0,0,0,0)
P3(1,1/√3,1/√6,0,0,0)
P4(1,1/√3,1/√6,1/√10,0,0)
P5(1,1/√3,1/√6,1/√10,√(2/5),0)
P6(1,1/√3,1/√6,1/√10,√(2/5),√(2/3))
cosθ=√(3/2)/{5/2+3/2}^1/2=√(3/2)√(1/4)=√(3/8)
===================================