A characterization of regular tetrahedra in Z^3

Details A characterization of regular tetrahedra in Z^3 A characterization of regular tetrahedra in Z^3

2007-12-23

arxiv.org/abs/0712.3951v2

Mathematics

Number Theory

10 pages, 4 figures

Scientific paper

In this note we characterize all regular tetrahedra whose vertices in R^3 have integer coordinates. The main result is a consequence of the characterization of all equilateral triangles having integer coordinates contained in previous work. Then we use this characterization to point out some corollaries. The number of such tetrahedra whose vertices are in the finite set {0,1,2,...,n}^3, n in N, is related to the sequence A103158 in the Online Encyclopedia of Integer Sequences.

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