On Pythagorean Pyramid we tried to build a tetrahedron out of four equal right angled triangles, but the attempt fell flat (pun intended!).

Is it possible to have a tetrahedron built out of right angled triangles, dropping the condition that all triangles be the same? Can you manage to have three equal faces? Or maybe two pairs of equal faces?

(In reply to Short answer to part 1. by broll)

If it's perpendicular to a side, is it going to be a tetrahedron? Won't it be either another rectangular solid on one hand, or something like a pup tent at the other extreme, or intermediately, something with even more faces, and in any event the plane of the cut will be a rectangle rather than a triangle.

Posted by Charlie on 2016-02-29 07:44:51