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Maximal Unit Lengths in 3D

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Put points in 3D space. What is the maximal number of unit lengths? For four points, it is obvious the maximal number is six unit lengths, using a tetrahedron. With five points, two joined tetrahedra give nine unit lengths.

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This Demonstration gives the following best-known solutions up to 20 points.

If you can find missed solutions matching or surpassing the best known maximum values, please send them to the author.

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Contributed by: Ed Pegg Jr and Thomas Rokicki (August 2016)
Open content licensed under CC BY-NC-SA

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The distances shown here are actually to make the points friendlier.

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