PERFECT CUBOID

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Perfect cuboid is an Euler brick having 

    PERFECT CUBOID
  • integer side lengths
  • integer face diagonal
  • integer space diagonal
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.

No perfect cuboid is known.

Equivalent to solution of Diophantine equations:
a2 + b2 = d2
a2 + c2 = e2
b2 + c2 = f2
Also an extra following equation has to be added:
a2 + b2 + c2 = g2 ( space diagonal equation )
where a, b, c are the edges and d, e, f are the diagonals. The space diagonal is g.

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