■サマーヴィルの等面四面体(その391)
n=5の場合,
P0(1/2,(√5)/2,0,(√10)/2)
P1(0,0,0,0)
P2(2,0,0,0)
P3(3/2,(√5)/2,(√10)/2,0)
P4(1,√5,0,0)
を
P0(m/2,m√5/2,0,m√10/2,h)
P1(0,0,0,0,0)
P2(0,0,0,0,5h)
P3(2m,0,0,0,4h)
P4(3m/2,m√5/2,m√10/2,0,3h)
P5(m,m√5,0,0,2h)
としてみる.
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P0P1^2=4m^2+h^2
P0P2^2=4m^2+16h^2
P0P3^2=6m^2+9h^2
P0P4^2=6m^2+4h^2
P0P5^2=4m^2+h^2
P1P2^2=25h^2
P1P3^2=4m^2+16h^2
P1P4^2=6m^2+9h^2
P1P5^2=6m^2+4h^2
P2P3^2=4m^2+h^2
P2P4^2=6m^2+4h^2
P2P5^2=6m^2+9h^2
P3P4^2=4m^2+h^2
P3P5^2=6m^2+4h^2
P4P5^2=4m^2+h^2
(その388)
h^2=1/5,m^2=6/5はこれらを満たす.
h^2=1/5,5h=√5 (△5の最短辺)
m^2の値からスケーリングができる.
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