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.
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