  Using ALMA observations of the C$^{18}$O(2-1) line emission of the gas
envelope of protostar L1527, we have reconstructed its morphology and
kinematics under the assumption of axisymmetry about the west-east axis. The
main original contribution to our understanding of the formation process of
L1527 is the presentation of a simple 3D parameterisation based solely on
regions that are not dominated by absorption. In the explored range ($\sim$0.7
to 5 arcsec from the star) the model reproduces observations better than
earlier attempts. The main results include: a measurement of the rotation
velocity that confirms its evolution to Keplerian toward short distances; a
measurement of the mean in-fall velocity, 0.43$\pm$0.10 kms$^{-1}$, lower than
free fall velocity, with no evidence for the significant $r$-dependence
suggested by an earlier analysis; a measurement of the central mass,
0.23$\pm$0.06 M$_{\odot}$ within a distance of 1.5 arcsec from the star, in
agreement with earlier estimates obtained from a different range of distances;
evidence for a strong disc plane depression of the in-falling flux resulting in
an $X$ shaped flow possibly caused by the freeze-out of CO molecules on dust
grains; a measurement of the accretion rate, 3.5$\pm$1.0 10$^{-7}$
M$_{\odot}$yr$^{-1}$ at a distance of 1 arcsec (140 au) from the star; evidence
for a 10$^\circ$ tilt of the symmetry plane of the envelope about the line of
sight, cancelling below $\sim$3 arcsec from the star, but matching infrared
observations and being also apparent on the sky map of the mean Doppler
velocity.
