■サマーヴィルの等面四面体(その348)

[1]G5

Q1Q2^2=81/50+3+9/50=90/50+3=24/5

Q1Q3^2=324/50+36/50=360/50=36/5

Q2Q3^2=81/50+3+9/50=90/50+3=24/5

 2:2:√6で,△4の2次元面G4と一致した.

  (n^2−1)/n=24/5・・・(OK)

 f^2=2(n+1)(n−2)/n=2・6・3/5=36/5

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[2]G6

Q2Q3^2=(147+343+350)/12^2=840/12^2

Q2Q4^2=(588+28+224+504)/12^2=1344/12^2

Q2Q5^2=(1323+63+126)/12^2=1512/12^2

Q3Q4^2=(147+175+14+504)/12^2=840^2

Q3Q5^2=(588+700+56)/12^2=1344/12^2

Q4Q5^2=(147+175+14+504)/12^2=840/12^2

  (n^2−1)/n=35/6=840/12^2・・・(OK)

 f^2=2(n+1)(n−2)/n=2・7・4/6=28/3=1344/14^2

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[まとめ]Fn,Gnでも次辺の長さはf^2=2(n+2)(n−1)/nで表される.

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