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tokens: at a distance of 1 arcsec (140 au) from the star. 5.6 Orientation in space The envelope thickness at y = 0, measured by an FWHM of ∼0.55 in λ (Fig. 10 , left) meaning ∼0.7 arcsec, is consistent with the value quoted in Section 3.1 from which an upper limit of ∼22° was placed on a possible tilt θ 2 between the disc plane and the ( y , z ) plane about the y -axis. The observed ∼10° tilt θ 1 about the z -axis of the map of 〈 V z 〉 that was mentioned in Section 3.2 and illustrated in Fig. 4 deserves some comments. As remarked then, such a tilt is also seen in the integrated flux for distances from the star exceeding ∼3 arcsec, not only in the present data (Figs 1 and 3 , left), but also in infrared observations (Tobin et al. 2008 ). The difference of inclination of the central part of the envelope, as measured from the integrated flux, and of the outer part, including the outflow, is not due to some trivial geometric effect but is real. Many factors may play a role in this context, such as magnetic field (see for example the review of Li et al. 2014 ) or binarity (Loinard et al. 2002 ). 6 SUMMARY In summary, the main original contribution of the present analysis to our understanding of the formation process of L1527 is the presentation of a simple 3D parametrization of the morphology and kinematics of the gas envelope based solely on the observation of the C 18 O (2–1) line emission from regions that are not dominated by absorption. In the explored range, the model, which uses eight relevant parameters, reproduces observations significantly better than earlier attempts. This was made possible by assuming central symmetry and axisymmetry about the x (west–east) axis and by excluding from the analysis Doppler velocities between 0 and 0.32 km s −1 and a band of the sky map of ±0.675 arcsec about the x -axis. Moreover we have reduced the radial dependences of the temperature and density to a single quantity, the effective emissivity. We have presented arguments showing that such assumptions are indeed reasonable. The main conclusions of the analysis are as follows. Rotation : the model uses successfully trajectories spiralling down towards the disc on paraboloids coaxial with it. We give evidence for the dominance of rotation over the explored range and confirm that the rotation curve is as expected from a transition from an inverse distance law to a Keplerian regime. The rotation velocity decreases from ∼1.66 to ∼0.34 km s −1 when r increases from 1 to 5 arcsec. However, the range explored is too distant from the star to allow direct observation of the disc. In-fall velocity : we measure a mean in-fall velocity of 0.43 ± 0.10 km s −1 over the explored range, smaller than free-fall velocity, with no evidence for a significant r -dependence, in particular no evidence for the sudden jump to ∼1.5 km s −1 required by Ohashi et al. ( 2014 ) to describe the absorption-dominated central region. Central mass : using simple arguments of energy conservation, we