  It is shown that the diameter $\diam (H^1_\mfr(R/I))$ of the first local
cohomology module of a tetrahedral curve $C= C(a_1,...,a_6)$ can be explicitly
expressed in terms of the $a_i$ and is the smallest non-negative integer $k$
such that $\mfr^k H^1_\mfr(R/I)=0$. From that one can describe all
arithmetically Cohen-Macaulay or Buchsbaum tetrahedral curves.
