An Infinite Family Of Perfect Parallelepipeds

Authors

Benjamin D. Sokolowsky, Bucknell University
Amy G. Vanhooft, The College at Brockport, State University of New York
Rachel M. Volkert, University of Northern IowaFollow
Clifford A. Reiter, Lafayette College

Document Type

Article

Journal/Book/Conference Title

Mathematics of Computation

Volume

83

Issue

289

First Page

2441

Last Page

2454

Abstract

A perfect parallelepiped has edges, face diagonals, and body diagonals all of integer length. We prove the existence of an infinite family of dissimilar perfect parallelepipeds with two nonparallel rectangular faces. We also show that we can obtain perfect parallelepipeds of this form with the angle of the nonrectangular face arbitrarily close to 90°. Finally, we discuss the implications that this family has on the famous open problem concerning the existence of a perfect cuboid. This leads to two conjectures that would imply no perfect cuboid exists.

Original Publication Date

1-1-2014

DOI of published version

10.1090/s0025-5718-2013-02791-3

Recommended Citation

Sokolowsky, Benjamin D.; Vanhooft, Amy G.; Volkert, Rachel M.; and Reiter, Clifford A., "An Infinite Family Of Perfect Parallelepipeds" (2014). Faculty Publications. 1447.
https://scholarworks.uni.edu/facpub/1447