  Medium resolution (lambda/Delta lambda = 5000-10000) VLT-ISAAC M-band spectra
are presented of 39 young stellar objects in nearby low-mass star forming
clouds showing the 4.67 micron stretching vibration mode of solid CO. By taking
advantage of the unprecedentedly large sample, high S/N ratio and high spectral
resolution, similarities in the ice profiles from source to source are
identified. It is found that excellent fits to all the spectra can be obtained
using a phenomenological decomposition of the CO stretching vibration profile
at 4.67 micron into 3 components. All observed interstellar CO profiles can
thus be uniquely described by a model depending on only 3 linear fit
parameters, indicating that a maximum of 3 specific molecular environments of
solid CO exist under astrophysical conditions. A simple physical model of the
CO ice is presented, which shows that the 2139.9 cm-1 component is
indistinguishable from pure CO ice. It is concluded, that in the majority of
the observed lines of sight, 60-90% of the CO is in a nearly pure form. In the
same model the 2143.7 cm-1 component can possibly be explained by the
longitudinal optical (LO) component of the vibrational transition in pure
crystalline CO ice which appears when the background source is linearly
polarised. Furthermore the absorption band from solid 13CO at 2092 cm-1 is
detected towards IRS 51 in the Rho Ophiuchi cloud complex and an isotopic ratio
of 12CO/13CO=68+/-10 is derived. It is shown that all the observed solid 12CO
profiles, along with the solid 13CO profile, are consistent with grains with an
irregularly shaped CO ice mantle simulated by a Continuous Distribution of
Ellipsoids (CDE), but inconsistent with the commonly used models of spherical
grains in the Rayleigh limit. [Abstract abridged]
