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On the second smallest ideal right-angled hyperbolic four-polytope
The regular ideal right-angled 24-cell has volume $4 π^2/3$ and is the unique minimum-volume entirely ideal right-angled hyperbolic four-polytope. We prove that the next distinct volume is $8 π^2/3$ and that its unique equality case is the reflection double of the 24-cell across one octahedral facet
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