  There are several works \cite{De} (and \cite{St}), \cite{En}, \cite{Co} and
\cite{Va} enumerating four-dimensional parallelotopes. In this work we give a
new enumeration showing that any four-dimensional parallelotope is either a
zonotope or the Minkowski sum of a zonotope with the regular 24-cell
$\{3,4,3\}$. Each zonotopal parallelotope is the Minkowski sum of segments
whose generating vectors form a unimodular system. There are exactly 17
four-dimensional unimodular systems. Hence, there are 17 four-dimensional
zonotopal parallelotopes. Other 35 four-dimensional parallelotopes are: the
regular 24-cell $\{3,4,3\}$ and 34 sums of the regular parallelotope with
non-zero zonotopal parallelotopes. For the nontrivial enumerating of the 34
sums we use a theorem discribing necessary and sufficient conditions when the
Minkowski sum of a parallelotope with a segment is a parallelotope.
