Euler Brick

An Euler brick, named for Leonhard Euler, is a rectangular cuboid, or box shape, whose three edge lengths and three face-diagonal lengths are all integers; a primitive Euler brick has edge lengths that share no common factor. A perfect Euler brick, whose space diagonal running corner to corner through the box is also an integer, has not yet been found. The condition defining an Euler brick is equivalent to solving a system of three Diophantine equations, one for each pair of edges and its corresponding face diagonal. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/