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Rational and Heron tetrahedra

MacDougall, James A. and Chisholm, C. (2006) Rational and Heron tetrahedra. Journal of Number Theory, 121 . pp. 153-185. (In Press)

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    Abstract

    Buchholz [R.H. Buchholz, Perfect pyramids, Bull. Austral. Math. Soc. 45 (1991) 353–368] began a systematic search for tetrahedra having integer edges and volume by restricting his attention to those with two or three different edge lengths. Of the fifteen configurations identified for such tetrahedra, Buchholz leaves six unsolved. In this paper we examine these remaining cases for integer volume, completely solving all but one of them. Buchholz also considered Heron tetrahedra, which are tetrahedra with integral edges, faces and volume. Buchholz described an infinite family of Heron tetrahedra for one of the configurations. Another of the cases yields a new infinite family of Heron tetrahedra which correspond to the rational points on a two-parameter elliptic curve.

    Item Type: Article
    Subjects: 00-xx General
    Faculty: UNSPECIFIED
    Depositing User: Stephanie
    Date Deposited: 18 Nov 2010 12:09
    Last Modified: 18 Nov 2010 12:09
    URI: https://docserver.carma.newcastle.edu.au/id/eprint/801

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