Tetrahedra

Tetrahedra, the analogue of triangles in the plane for three-dimensional Euclidean space, are surprisingly unstudied considering their "seeming" simplicity. To give you the flavor of the kinds of questions to be looked at, do you think you can construct a tetrahedron with edge lengths?

a. 7, 4, 4, 4, 4, 4 b. 18, 17, 16, 13, 13, 13

Throughout our discussion, lengths will refer to Euclidean distances. I will discuss the particularly interesting situation where potential edge lengths are positive integers; remember that the edges (sides) of a tetrahedron can have positive real numbers for lengths.