tetramagic19

The Graph K_4, i.e. the vertexes and the edges of a tetrahedron is unfortunately not edge magic: It is not possible to assign the numbers 1,2,...,10 to the vertexes and edges in a way that all sums u + uv + v for all vertexes  u,v and uv the edge connecting u and v are equal.
However, if we include 11 and do not use one of the other numbers, we find 20 different solutions of the problem. The tetrahedron stub model shows one of them: 7, 9,10,11 are located at the vertexes for the common edge sum 22.
Some fancy inner "bones" were added just for fun.