A characterization of regular tetrahedra in Z^3
Number Theory
2007-12-31 v2 Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.0712.3951,
title = {A characterization of regular tetrahedra in Z^3},
author = {Eugen J. Ionascu},
journal= {arXiv preprint arXiv:0712.3951},
year = {2007}
}
Comments
10 pages, 4 figures