
A "Perfect Pyramid" is defined to be an integer sided tetrahedron with integer face areas and integer volume. Given all these constraints one would expect them to be quite rare ... and of course they are. An exhaustive search over all possible tetrahedra with integer sides less than 157 revealed only the above example which has a volume of 18144. Despite this, it turns out that there are infinitely many such beasts. See Perfect Pyramids for more details. 
Ralph Buchholz
27 March 2001