■サマーヴィルの等面四面体(その381)
△4
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
4m^2+h^2(5)<4m^2+16h^2(2)
6m^2+4h^2(4)<6m^2+9h^2(3)
25h^2(1)
G7は
P2P3=P3P4=P4P5=P5P6=P6P7=√7
P2P4=P3P5=P4P6=P5P7=√12
P2P5=P3P6=P4P7=√15
P2P6=P3P7=4
P2P7=√15
4m^2+h^2=7
6m^2+4h^2=12
6m^2+9h^2=25h^2=15
4m^2+16h^2=16
h^2=3/5,m^2=8/5
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