An infinite family of perfect parallelepipeds
Mathematics of Computation
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
DOI of published version
Sokolowsky, Benjamin D.; Vanhooft, Amy G.; Volkert, Rachel M.; and Reiter, Clifford A., "An infinite family of perfect parallelepipeds" (2014). Faculty Publications. 1447.