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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Perfect parallelepipeds exist
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by Jorge F. Sawyer and Clifford A. Reiter PDF
Math. Comp. 80 (2011), 1037-1040 Request permission


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:
  • Clifford A. Reiter
  • Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042
  • Email:
  • 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:
  • MathSciNet review: 2772108