RK Guy, Unsolved Problems In Number Theory, problem D22: Simplexes with rational content. "Are there simplexes in any number of dimensions, all of whose contents (lengths, areas, volumes, hypervolumes) are rational?" Ralph Heiner Buchholz: Perfect pyramids, Bulletin of the Australian Mathematical Society 45,3 (1992) 353-368 proves an infinite number of Heronian tetrahedra exist. Randall L. Rathbun [randall AT ncr-sd.UUCP] in 1987 made a huge database of Heronian triangles. He wanted to find one with rational medians. He failed, but claims with Buchholz to have a proof using Somos(5) sequences (!!) that an infinite number of Heronian triangles with two rational medians exist. He gives as examples Sides Medians Area 73 51 26 sqrt(3796) 48.5 17.5 420 875 626 291 sqrt(557580.25) 572 216.5 55440 A proof appeared here showing how every rational point on a certain elliptic curve corresponded to such a triangle: Ralph H. Buchholz & Randall L. Rathbun: Heron Triangles And Elliptic Curves, Bull. Australian Math. Soc 58 (1998) 411-421 They conjecture there are no Heronian triangles with all 3 medians rational.