■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

===================================

 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)

===================================