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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
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

Clifford A. Reiter
Affiliation: Department of Mathematics, Lafayette College, Easton, Pennsylvania 18042

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.

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