  Sperm modulate their flagellar symmetry to navigate through complex
physico-chemical environments and achieve reproductive function. Yet it remains
elusive how sperm swim forwards despite the inherent asymmetry of several
components that constitutes the flagellar engine. Despite the critical
importance of symmetry, or the lack of it, on sperm navigation and its
physiological state, there is no methodology to date that can robustly detect
the symmetry state of the beat in free-swimming sperm in 3D.How does symmetric
progressive swimming emerge even for asymmetric beating, and how can beating
(a)symmetry be inferred experimentally? Here, we numerically resolve the fluid
mechanics of swimming around asymmetrically beating spermatozoa. This reveals
that sperm spinning critically regularizes swimming into persistently symmetric
paths in 3D, allowing sperm to swim forwards despite any imperfections on the
beat. The sperm orientation in three-dimensions, and not the swimming path, can
inform the symmetry state of the beat, eliminating the need of tracking the
flagellum in 3D. We report a surprising correspondence between the movement of
sperm and spinning-top experiments, indicating that the flagellum drives
''spinning-top'' type rotations during sperm swimming, and that this parallel
is not a mere analogy. These results may prove essential in future studies on
the role of (a)symmetry in spinning and swimming microorganisms and
micro-robots, as body orientation detection has been vastly overlooked in
favour of swimming path detection. Altogether, sperm rotation may provide a
foolproof mechanism for forward propulsion and navigation in nature that would
otherwise not be possible for flagella with broken symmetry.
