2007/12/23 by Eugen J. Ionaşcu, Eugen J. Ionascu, Ionascu, Eugen J. · 8 citations
Chemistry · Engineering · Mathematics · #Analytic Number Theory Research #Characterization (materials science) #Chemistry #Combinatorics #Computer science #Discrete mathematics #Equilateral triangle #Geometry #Integer (computer science) #Mathematics #Mathematics and Applications #Physics #Point (geometry) #Sequence (biology) #Set (abstract data type) #Tetrahedron #graph theory and CDMA systems #math.CO #math.NT #msc:11A67
paper · pdf · doi:10.48550/arxiv.0712.3951
published in arXiv (Cornell University) (Cornell University) · 10 pages, 4 figures
openalex publication_date 2007/12/23 · arxiv created 2007/12/31 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.