integer brick | integer cuboid

A perfect cuboid is a cuboid having integer side lengths, integer face diagonals d_(a b) | = | sqrt(a^2 + b^2) d_(a c) | = | sqrt(a^2 + c^2) d_(b c) | = | sqrt(b^2 + c^2), and an integer space diagonal d_(a b c) = sqrt(a^2 + b^2 + c^2). The problem of finding such a cuboid is also called the brick problem, diagonals problem, perfect box problem, perfect cuboid problem, or rational cuboid problem.

cuboid | Diophantine equation | Euler brick | face diagonal | Heronian tetrahedron | Heronian triangle | integer triangle | space diagonal