Right Tetrahedra and Pythagorean Quadruples
A right tetrahedron, also known as trirectangular tetrahedron, is a tetrahedron with three right angled triangles and a base triangle. By studying Pythagorean triples and quadruples, we deduce the existence of different types of right tetrahedra. Three cases of right tetrahedra are the focus of this paper: (i) Right tetrahedra with all integer edges (ii) Right tetrahedra with integer face areas, and (iii) Right tetrahedra with integer face areas and integer principal edges. Case (iii) constitutes the original work of this paper. The constructive method we use for this case allow us to classify existence of such tetrahedra as well as provide an algorithm to find those integer values from a given set of Pythagorean quadruple.