Abstract:There are parallelepipeds with edge lengths, face diagonal lengths and body diagonal lengths that are all positive integers. In particular, there is a parallelepiped with edge lengths $271$, $106$, $103$, minor face diagonal lengths $101$, $266$, $255$, major face diagonal lengths $183$, $312$, $323$, and body diagonal lengths $374$, $300$, $278$, $272$. Focused brute force searches give dozens of primitive perfect parallelepipeds. Examples include parallellepipeds with up to two rectangular faces.
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- Jorge F. Sawyer
- Affiliation: Box 8681 Farinon Center, Lafayette College, Easton, Pennsylvania 18042
- Email: email@example.com
- Clifford A. Reiter
- Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
- Email: firstname.lastname@example.org
- Received by editor(s): November 16, 2009
- Received by editor(s) in revised form: December 3, 2009
- Published electronically: August 17, 2010
- Additional Notes: The support of a Lafayette EXCEL grant is appreciated
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
- Journal: Math. Comp. 80 (2011), 1037-1040
- MSC (2010): Primary 11D09
- DOI: https://doi.org/10.1090/S0025-5718-2010-02400-7
- MathSciNet review: 2772108