Find two regular tetrahedra that share a face placed in a way such that each vertex has integer coordinates.
okay... playing around on the back of a napkin...
it occurs to me that...
two tetrahedrons... one at:
(0,0,0)
(0,12,12)
(12,0,12)
(12,12,0)
and the other at
(0,12,12)
(12,0,12)
(12,12,0)
(16,16,16)
of course they both share the face:
(0,12,12)
(12,0,12)
(12,12,0)
and the tetrahedrons have an edge of length 12√2.
We can also shift, scale, and rotate this around to produce an infinite number of others....
solution
