We use a homogeneous sample of about 1100 optical and radio rotation curves (RCs) and relative surface photometry to investigate the main mass structure properties of spirals, over a range of 6 mag and out to ≾ 1.5 and 2 optical radii (for the optical and radio data, respectively). We confirm the strong dependence on luminosity for both the profile and the amplitude of RCs claimed by Persic & Salucci. Spiral RCs show the striking feature that a single global parameter, e.g. luminosity, dictates the rotational velocity at any radius for any object, so revealing the existence of a universal RC. At high luminosities, there is a slight discrepancy between the profiles of RCs and those predicted from the luminous matter (LM) distributions: this implies a small, yet detectable, amount of dark matter (DM). At low luminosities, the failure of the LM prediction is much more severe, and the DM is the only relevant mass component. We show that the universal RC implies a number of scaling properties between dark and luminous galactic structure parameters: (i) the DM/LM mass ratio scales inversely with luminosity; (ii) the central halo density scales as L-0.7; (iii) the halo core radius is comparable to the optical radius, but shrinks for low luminosities; (iv) the total halo mass scales as L0.5. Such scaling properties can be represented as a curve in the (luminosity)-(DM/LM mass ratio)-(DM core radius)-(DM central density) space, which provides a geometrical description of the tight coupling between the dark and the luminous matter in spiral galaxies.