Readers familiar with the nine-point circle property of a triangle (Figure 1) may have wondered whether there is a similar result for a tetrahedron.

In general the answer is “No”: there is no equivalent of the orthocentre for a tetrahedron, since the altitudes from the vertices onto the opposite faces do not intersect. There is, however, a special kind of tetrahedron for which these four lines do have a point H in common.