  A new classification of circular polarization C points in three-dimensional
polarization ellipse fields is proposed. The classification type depends on the
out-of-plane variation of the polarization ellipse axis, in particular, whether
the ellipse axes are in the plane of circular polarization one or three times.
A minimal set of parameters for this classification are derived, and discussed
in the context of the familiar in-plane C point classification into lemon,
star, and monstar types. This new geometric classification is related to the
M\"obius index of polarization singularities recently introduced by Freund.
