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added link to Helly's theorem
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Kevin O'Bryant
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If you mean "any four lie in some ball of radius 1", then the same holds for all five points due to Helly theoremHelly's theorem (the unit balls centered in these points must have a common point).

If you mean "any four lie in some ball of radius 1", then the same holds for all five points due to Helly theorem (the unit balls centered in these points must have a common point).

If you mean "any four lie in some ball of radius 1", then the same holds for all five points due to Helly's theorem (the unit balls centered in these points must have a common point).

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Fedor Petrov
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If you mean "any four lie in some ball of radius 1", then the same holds for all five points due to Helly theorem (the unit balls centered in these points must have a common point).