■サマーヴィルの等面四面体(その434)
1−cp/1−cq/1−cr/1−cs
では
=1−cp/1−cq/(1−cr/(1−cs))
=1−cp/1−cq(1−cs)/(1−cs−cr)
=1−cp(1−cs−cr)/{(1−cs−cr)−cq(1−cs)}
={{(1−cs−cr)−cq(1−cs)}−cp(1−cs−cr)}/{(1−cs−cr)−cq(1−cs)}
cp=1/4,cq=1/4,cr=1/4とおくと
={{16−16cs−4−(4−4cs))}−(4−4cs−1)}/{(16−16cs−4)−(4−4cs)}
=(5−8cs)/(8−12cs0
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cs=cos^2π/s=5/8のとき,
1−cp/1−cq/1−cr/1−cs=0
π/s=arccos(√(5/8))
s=π/arccos(√(5/8))=4.76679
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