Perfect Parallelepipeds

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A perfect parallelepiped is a parallelepiped with integer length edges, face diagonals, and body diagonals. In 2009 it was shown that perfect parallelepipeds exist. This Demonstration gives 10 examples together with their generating vectors and required lengths.
Contributed by: Jorge F. Sawyer (March 2011)
Open content licensed under CC BY-NC-SA
Snapshots
Details
J. F. Sawyer and C. A. Reiter, "Perfect Parallelepipeds Exist," arXiv, 2009.
Permanent Citation
"Perfect Parallelepipeds"
http://demonstrations.wolfram.com/PerfectParallelepipeds/
Wolfram Demonstrations Project
Published: March 7 2011