  We give a new manifestly natural presentation of the supergravity c-map. We
achieve this by giving a more explicit description of the correspondence
between projective special K\"ahler manifolds and variations of Hodge
structure, and by demonstrating that the twist construction of Swann, for a
certain kind of twist data, reduces to a quotient by a discrete group. We
combine these two ideas by showing that variations of Hodge structure give rise
to the aforementioned kind of twist data and by then applying the twist
realisation of the c-map due to Macia and Swann. This extends previous results
regarding the lifting of general isomorphisms along the undeformed c-map, and
of infinitesimal automorphisms along the deformed c-map. We show in fact that
general isomorphisms can be naturally lifted along the deformed c-map.
