  It is well known that the three altitudes of a triangle are concurrent at the
so-called orthocenter of the triangle. So one might expect that the altitudes
of a tetrahedron also meet at a point. However, it was already pointed out in
1827 by the Swiss geometer Jakob Steiner (1796--1863) that the altitudes of a
general tetrahedron are mutually skew, for they are generators of an
equilateral hyperboloid.
