■DE群多面体の面数公式(その841)
321の頂点間距離が2のとき,半径は√3
R^2=1+1/3+1/6+1/10+1/15+1/21+a7^2=3
=1+1/3+1/6+1/10+1/15+2/6+b7^2
1+1/3+1/6+1/10+1/15=(30+10+5+3+2)/=5/3
R^2=5/3+1/3+b7^2=5/3+1/21+a7^2=3
a7^2=(63−35−1)/21=9/7
b7^2=(9−5−1)/3=1
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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))
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)
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