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?
It is possible for all 4 faces of a tetrahedron be right angles and have all six edges distinct integers.
Right angles are ABC, BCD, ABD, ACD
AB=672, BC=104, CD=153, AC=680, BD=185, AD=697