WOLFRAM|DEMONSTRATIONS PROJECT

Regular Tetrahedra Formed by Lattice Points Equidistant from the Origin

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pick a tetrahedron
1
norm = 1
3
edge length = 2
2
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 (
(x,y,z)
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
(2n-1)
3
.