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Mathematics of Computation

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Perfect parallelepipeds exist


Authors: Jorge F. Sawyer and Clifford A. Reiter
Journal: Math. Comp. 80 (2011), 1037-1040
MSC (2010): Primary 11D09
DOI: https://doi.org/10.1090/S0025-5718-2010-02400-7
Published electronically: August 17, 2010
MathSciNet review: 2772108
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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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Additional Information

Jorge F. Sawyer
Affiliation: Box 8681 Farinon Center, Lafayette College, Easton, Pennsylvania 18042
Email: sawyerj@lafayette.edu

Clifford A. Reiter
Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
Email: reiterc@lafayette.edu

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
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.