Perfect Parallelepipeds Exist
Number Theory
2009-12-15 v2
Abstract
There are parallelepipeds with edge lengths, face diagonal lengths and body diagonal lengths 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.
Keywords
Cite
@article{arxiv.0907.0220,
title = {Perfect Parallelepipeds Exist},
author = {Jorge F. Sawyer and Clifford A. Reiter},
journal= {arXiv preprint arXiv:0907.0220},
year = {2009}
}
Comments
Minor revision: new example