Mr. Belvedere's proctor tells him that when he assembles the puzzle it forms an almost perfect "cube". A cube has the same dimensions on all sides. What he puts together is a geometrical Orthotope or Box.
If Mr. Belvedere had only a few weeks of formal education as a child, how could he have set a pole vault record, presumably at Clemens, of 14" 4" in 1922? Actually, that world record height was set in 1932.
Dr. Keating forbids Mr. Belvedere from using his enrollment at Clemens University for any form of notoriety or publicity. However this would not remotely be in the colleges best interest, especially a private one, because high caliber students or faculty is a sure way to gain more enrollment and larger endowments.