  Aims. We investigate the relationships between three main optical galaxy
observables (spectral properties, colours, and morphology), exploiting the data
set provided by the COSMOS/zCOSMOS survey. The purpose of this paper is to
define a simple galaxy classification cube, using a carefully selected sample
of around 1000 galaxies. Methods. Using medium resolution spectra of the first
1k zCOSMOS-bright sample, optical photometry from the Subaru/COSMOS
observations, and morphological measurements derived from ACS imaging, we
analyze the properties of the galaxy population out to z~1. Applying three
straightforward classification schemes (spectral, photometric, and
morphological), we identify two main galaxy types, which appear to be linked to
the bimodality of galaxy population. The three parametric classifications
constitute the axes of a "classification cube". Results. A very good agreement
exists between the classification from spectral data (quiescent/star-forming
galaxies) and that based on colours (red/blue galaxies). The third parameter
(morphology) is less well correlated with the first two: in fact a good
correlation between the spectral classification and that based on morphological
analysis (early-/late-type galaxies) is achieved only after partially
complementing the morphological classification with additional colour
information. Finally, analyzing the 3D-distribution of all galaxies in the
sample, we find that about 85% of the galaxies show a fully concordant
classification, being either quiescent, red, bulge-dominated galaxies (~20%) or
star-forming, blue, disk-dominated galaxies (~65%). These results imply that
the galaxy bimodality is a consistent behaviour both in morphology, colour and
dominant stellar population, at least out to z~1.
