Regular Tetrahedra Formed by Lattice Points Equidistant from the Origin

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From an integer lattice, pick four points at the same distance from the origin (called the norm) that determine the vertices of a regular tetrahedron. Add the condition that the set of all 12 coordinates ( for each of the four vertices) does not have a common factor. Solutions we have found so far always appear to have a norm of the form .

Contributed by: Ed Pegg Jr (January 2017)
Open content licensed under CC BY-NC-SA


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