  I discuss uniform, isotropic, plane, singly connected, electrically linear,
regular symmetric Hall-plates with an arbitrary number of N peripheral contacts
exposed to a uniform perpendicular magnetic field of arbitrary strength. In
practice, the regular symmetry is the most common one. If the Hall-plates are
mapped conformally to the unit disk, regular symmetry means that all contacts
are equally large and all contacts spacings are equally large, yet the contacts
spacings may have a different size than the contacts. Such Hall-plates do not
change when they are rotated by 360{\deg}/N. Their indefinite conductance
matrices are circulant matrices, whose complex eigenvalues are computable in
closed form. These eigenvalues are used to discuss the Hall-output voltage, the
maximum noise-efficiency, and Van-der-Pauw's method for measuring sheet
resistances. For practical use, I report simple approximations for Hall-plates
with four contacts and 90{\deg} symmetry with popular shapes like disks,
rectangles, octagons, squares, and Greek crosses with and without rounded
corners.
