■サマーヴィルの等面四面体(その900)

 △3,F4,Z∞について計算したが,引き続きG5,H6を求めたい.

[1]a^2:b^2:c^2=5:8:9

  (e^2+t^2)/(e^2+4t^2)=5/8

  8(e^2+t^2)=5(e^2+4t^2)

  e^2=4t^2,t^2=e^2/4

  c^2=9e^2/4

[2]a^2:b^2:c^2=6:10:12

  (e^2+t^2)/(e^2+4t^2)=6/10

  5(e^2+t^2)=3(e^2+4t^2)

  2e^2=7t^2,t^2=2e^2/7

  c^2=18e^2/7

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[まとめ]

△3 :(a^2,b^2,c^2)=(9/8,12/8,9/8)e^2

F4 :(a^2,b^2,c^2)=(6/5,9/5,9/5)e^2

G5 :(a^2,b^2,c^2)=(5/4,8/4,9/4)e^2

H6 :(a^2,b^2,c^2)=(9/7,18/7,18/7)e^2

Z∞:(a^2,b^2,c^2)=(3/2,6/2,9/2)e^2

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