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A Tetrahedron with Rational sides, Face Areas, and Volume. The smallest examples have pairs of opposite sides (148, 195, 203), (533, 875, 888), (1183, 1479, 1804), (2175, 2296, 2431), (1825, 2748, 2873), (2180, 2639, 3111), (1887, 5215, 5512), (6409, 6625, 8484), and (8619, 10136, 11275).
See also Heron's Formula, Heronian Triangle
References
Guy, R. K. ``Simplexes with Rational Contents.'' §D22 in
Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 190-192, 1994.