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

Entropy and complexity analysis of the D-dimensional rigid rotator and hyperspherical harmonics