  The flattening rotation velocity $v(r)\to {\rm constant}$ found by Vera Rubin
and collaborators and very apparent in the SPARC galaxy-rotation data coincides
with Kepler's law in one less dimension. Thus, it is naturally reproduced by
elongated dark matter distributions with the axis of prolateness perpendicular
to the galactic plane. This theoretical understanding is borne out by the
detailed fits to the rotation data that we here report: for equal dark matter
profile, elongated distributions provide smaller $\chi^2$ than purely spherical
ones. We also propose to use the geometric mean of the individual halo
ellipticities, as opposed to their arithmetic average, because $s=c/a\in
(0,\infty)$ corresponds to spherical haloes for $s=1$, so that the usually
reported average is skewed towards oblateness and fails to reveal the large
majority of prolate haloes. Several independently coded fitting exercises
concur in yielding $s<1$ for most of the database entries and the oblate
exceptions are understood and classified. This likely prolateness is of
consequence for the estimated dark matter density near Earth.
