Find two regular tetrahedra that share a face placed in a way such that each vertex has integer coordinates.

I started with the tetrahedron with vertices (0,0,0), (1,1,0), (1,0,1) and (0,1,1). The symmetrical image of (0,0,0) with regard to the opposite face turns out to be (4/3, 4/3, 4/3), so multyplying everything by 3 gets:

(0,0,0), (3,3,0), (3,0,3), (0,3,3)

and

(4,4,4), (3,3,0), (3,0,3), (0,3,3)

Posted by e.g. on 2004-03-25 14:56:25