If a tetrahedron is constructed on a base with side lengths 125, 244, 267, then the remaining sides can take the shapes of three right triangles: (44, 240, 244), (44, 117, 125), (117, 240, 267).
And now the sum of the squares of the lengths of each pair of opposite sides in the tetrahedron is the same:
1172 + 2442 = 1252 + 2402 = 442 + 2672 = 73225
(From Edward Barbeau, Power Play, 1997.)