A useful minimal "Heronian" tetrahedron with integer edge-lengths, face-areas, volume etc (due to Rathbun?) is given at http://mathworld.wolfram.com/HeronianTetrahedron.html Warning: the sides have been shuffled on that page: for consistency with other examples given there, they should instead be re-ordered as 51 52 53 80 117 84 . Furthermore the areas and volume given there are bizarrely garbled [although correct for other examples, with the ordering repaired] --- they should actually read 1170, 1890, 2016, 1800 (in some order); 18144 [is Eric Weisstein online?]. To utilise this as a test-case requires coordinates: one pose has vertices [w,x,y,z] = [1,0,0,0], [1,51,0,0], [17,416,780,0], [1105,-43680,63756,-51408], where a point has Cartesian coordinate [x/w, y/w, z/w] ; and faces [d,a,b,c] = [0,0,0,1], [0,0,204,-253], [0,45,24,-68], [835380,-16380,9471,20128], where a plane has equation a x + b y + c z + d w = 0 . Almost certainly, a cunningly chosen isometry would reduce the size of these components substantially; but I don't have any ideas about a good algorithm for finding the optimal pose. Any ideas, anybody? Fred Lunnon