  Rapidly rotating stars have been recently recognized as having a major role
in the interpretation of colour-magnitude diagrams of young and
intermediate-age star clusters in the Magellanic Clouds and in the Milky Way.
In this work, we evaluate the distinctive spectra and distributions in
colour-colour space that follow from the presence of a substantial range in
effective temperatures across the surface of fast rotators. The calculations
are inserted in a formalism similar to the one usually adopted for non-rotating
stars, which allows us to derive tables of bolometric corrections as a function
not only of a reference effective temperature, surface gravity and metallicity,
but also of the rotational speed with respect to the break-up value, $\omega$,
and the inclination angle, $i$. We find that only very fast rotators
($\omega>0.95$) observed nearly equator-on ($i>45^\circ$) present sizable
deviations from the colour-colour relations of non-rotating stars. In light of
these results, we discuss the photometry of the $\sim$ 200-Myr-old cluster NGC
1866 and its split main sequence, which has been attributed to the simultaneous
presence of slow and fast rotators. The small dispersion of its stars in
colour-colour diagrams allow us to conclude that fast rotators in this cluster
either have rotational velocities $\omega<0.95$, or are all observed nearly
pole-on. Such geometric colour-colour effects, although small, might be
potentially detectable in the huge, high-quality photometric samples in the
post-Gaia era, in addition to the evolutionary effects caused by
rotation-induced mixing.
