  In "Unsolved Problems in Number Theory" problem D22 Richard Guy asked for the
existence of simplices with integer lengths, areas, volumes... In dimension two
this is well known, these triangles are called Heron triangles.
  Here I will present my results on Heron tetrahedra, their connection to the
existence of an integer box (problem D18), the tools for the search for higher
dimensional Heron simplices and my nice embedding conjecture about Heron
simplices, which I can only proof in dimension two, but I verified it for a
large range in dimension three.
