  Flux-periodic oscillations of the superconducting gap in proximitized
core-shell nanowires are explored. Periodicity of oscillations in the energy
spectrum of a cylindrical nanowire is compared with nanowires having hexagonal
and square cross-section geometry, along with the effects of Zeeman and Rashba
spin-orbit interaction. A transition between h/e and h/2e periodicity is found
and shown to be dependent on the chemical potential, with correspondence to
degeneracy points of the angular momentum quantum number. For a thin shell of a
square nanowire, solely h/e periodicity is found in the infinite wire spectrum
and shown to result from energy separation between the lowest groups of excited
states.
