A characterization of regular tetrahedra in Z³

2007/12/23 by Eugen J. Ionaşcu, Eugen J. Ionascu, Ionascu, Eugen J.
Engineering · Mathematics · #Analytic Number Theory Research #Mathematics and Applications #graph theory and CDMA systems #math.CO #math.NT #msc:11A67

paper · pdf · doi:10.48550/arxiv.0712.3951

10 pages, 4 figures

arxiv created 2007/12/31 · arxiv updated 2009/12/01

Abstract

In this note we characterize all regular tetrahedra whose vertices in R³ 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,...,n³, n in N, is related to the sequence A103158 in the Online Encyclopedia of Integer Sequences.

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