■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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