■DE群多面体の面数公式(その520)
D群ではR^2=n/2となっている.D3〜D8が入れ子構造をなしていると仮定して計算してみたい.
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[1]D3
R^2=1+1/3+a3^3=3/2
a3^2=(9−8)/6=1/6
R^2=1+b2^2+b3^2=3/2
b3^2=1/2
b2^2=(9−6−3)/6=0
[2]D4
R^2=1+1/3+1/6+a4^2=4/2
a4^2=(12−6−2−1)/6=3/6
R^2=1+1/3+b3^2+b4^2=4/2
b4^2=1/2
b3^2=(12−6−2−3)/6=1/6
[3]D5
R^2=1+1/3+1/6+1/10+a5^2=5/2
=1+1/3+1/6+2/4+b5^2
R^2=9/6+2/4+b5^2=9/6+1/10+a5^2=5/2
a5^2=(150−90−6)/60=54/60
b5^2=(150−90−30)/60=30/60=(1/√2)^2
[4]D6
R^2=1+1/3+1/6+1/10+1/15+a6^2=6/2
=1+1/3+1/6+1/10+b5^2+b6^2
b6^2=1/2と考えられる.
R^2=48/30+1/2+b6^2=48/30+1/15+a6^2=6/2
a6^2=(90−48−2)/30=40/30
b5^2=(90−48−15)/30=27/30
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