■サマーヴィルの等面四面体(その805)

△6は

  P0P1=P1P2=P2P3=P3P4=P4P5=P5P6=√6

  P0P2=P1P3=P2P4=P3P5=P4P6=√10

  P0P3=P1P4=P2P5=P3P6=√12

  P0P4=P1P5=P2P6=√12

  P0P5=P1P6=√10

  P0P6=√6

5m^2+h^2(6)<5m^2+25h^2(2)

8m^2+4h^2(5)<8m^2+16h^2(3)

9m^2+9h^2(4)

36h^2(1)

5m^2+h^2=6,5m^2+25h^2=10

8m^2+4h^2=10,8m^2+16h^2=12

9m^2+9h^2=12

36h^2=6

h^2=1/6,m^2=7/6

△5(0,0,0,0,0,0),(−5,1,1,1,1,1),(−4,−4,2,2,2,2),(−3,−3,−3,3,3,3),(−2,−2,−2,−2,4,4),(−1,−1,−1,−1,−1,5)

 △5上に構成しているから,m^2=6

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[1]n=3の本体

  9h^2=2m^2+h^2=3,h^2=1/3,m^2=4h^2=4/3

  m^2=3

[2]n=4の本体

  16h^2=3m^2+h^2=4,h^2=1/4,m^2=5h^2=5/4

  m^2=4

[3]n=5の本体

  25h^2=4m^2+h^2=5,h^2=1/5,m^2=6h^2=6/5

  m^2=5

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