The center of a tetrahedron is the intersection of the lines from a
vertex to the center of the opposite side. At least, in 3DLDF, this is
the center of a Tetrahedron. I'm not 100 degrees
certain
that this is mathematically correct.
Tetrahedron t(origin, 4);
t.draw();
t.get_center().dotlabel("$c$");
Fig. 39.