  In this paper we carry out an information-theoretic analysis of the
$D$-dimensional rigid rotator by studying the entropy and complexity measures
of its wavefunctions, which are controlled by the hyperspherical harmonics.
These measures quantify single and two-fold facets of the rich intrinsic
structure of the system which are manifest by the intricate and complex variety
of D-dimensional geometries of the hyperspherical harmonics. We calculate the
explicit expressions of the entropic moments and the R\'enyi entropies as well
as the Fisher-R\'enyi, Fisher-Shannon and LMC complexities of the system. The
explicit expression for the last two complexity measures is not yet possible,
mainly because the logarithmic functional of the Shannon entropy has not yet
been obtained up until now in a closed for
