  The s-lecture hall polytopes P_s are a class of integer polytopes defined by
Savage and Schuster which are closely related to the lecture hall partitions of
Eriksson and Bousquet-M\'elou. We define a half-open parallelopiped Par_s
associated with P_s and give a simple description of its integer points. We use
this description to recover earlier results of Savage et al. on the
\delta-vector (or h^*-vector) and to obtain the connections to s-ascents and
s-descents, as well as some generalizations of these results.
