What question did this study set out to answer?

The research aims to prove that no rectangular parallelepiped can exist with integer edges, face diagonals, and space diagonals.

March 27, 2026Open Access

No Perfect Cuboid Exists

Key Points

The research aims to prove that no rectangular parallelepiped can exist with integer edges, face diagonals, and space diagonals.
Mathematical proof using geometric principles
Analysis of integer conditions for edges and diagonals
No configuration satisfies the conditions for a rectangular parallelepiped with integer measurements.
The proof establishes limits in the construction of such geometric shapes.

Abstract

Preprint v1 — A proof that no rectangular parallelepiped with all integer edges, face diagonals, and space diagonal exists. Abstract redacted pending IP review. Full abstract and unrestricted access will be available in v2 upon completion of intellectual property proceedings. Author: Joseph Keen Affiliation: Phoenix Quantum Labs LLC

Connected Papers

Building similarity graph...

Analyzing shared references across papers

Discussion

Cite this study

Joseph R. Keen (Wed,) studied this question.

www.synapsesocial.com/papers/69c620be15a0a509bde19556 — DOI: https://doi.org/10.5281/zenodo.19216669

No Perfect Cuboid Exists

Key Points

Abstract

Citation Network

Connected Papers

Discussion

Cite this study

Social Feed

Authors

Actions

References and Citations

Citation Network

Connected Papers

Discussion

Also consider