We selected a sample of 437 BL Lac objects, taken from the RomaBZCat catalogue, for which spectroscopic information and SDSS photometry is available. We propose a new classification of BL Lacs in which the sources type is not defined only on the basis of the peak frequency of the synchrotron component in their Spectral Energy Distribution (types L and H), but also on the relevance of this component with respect to the brightness of the host galaxy (types N and G, for nuclear or galaxy dominated sources). We found that the SDSS colour index u-r=1.4 is a good separator between these two types. We used multiband colour-colour plots to study the properties of the BL Lac classes and found that in the X-ray to radio flux ratio vs u-r plot most of the N (blue) sources are located in a rather narrow strip, while the G-sources (red) are spread in a large area, and most of them are located in galaxy clusters or interacting systems, suggesting that their X-ray emission is not from a genuine BL Lac nucleus but it is related to their environment. Of the about 135 sources detected in the gamma-rays by Fermi-GST, nearly all belong to the N-type, indicating that only this type of sources should be considered as genuine BL Lac nuclei. The J-H, H-K plot of sources detected in the 2MASS catalogue is consistent with that of the bona fide BL Lac objects, independently of their N or G classification from the optical indices, indicating the existence in G-type sources of a K-band excess possibly due to a steep, low frequency peaked emission which deserves further investigations. We propose to use these colour plots as a further tool for searching candidate counterparts of newly discovered high-energy sources.
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