Editing Parallelepiped (section)

==Perfect parallelepiped==

A ''perfect parallelepiped'' is a parallelepiped with integer-length edges, face diagonals, and [[space diagonal]]s.  In 2009, dozens of perfect parallelepipeds were shown to exist,<ref>{{Cite journal|first1=Jorge F.|last1=Sawyer|first2=Clifford A.|last2=Reiter|year=2011|title=Perfect Parallelepipeds Exist|journal=[[Mathematics of Computation]]|volume=80|issue=274|pages=1037–1040|arxiv=0907.0220|doi=10.1090/s0025-5718-2010-02400-7|s2cid=206288198}}.</ref>  answering an open question of [[Richard K. Guy|Richard Guy]]. One example has edges 271, 106, and 103, minor face diagonals 101, 266, and 255, major face diagonals 183, 312, and 323, and space diagonals 374, 300, 278, and 272. 

Some perfect parallelepipeds having two rectangular faces are known. But it is not known whether there exist any with all faces rectangular; such a case would be called a perfect [[cuboid]].