Context : The southern long-period Cepheid RS Pup is surrounded by a large circumstellar dusty nebula reflecting the light from the central star .
Due to the changing luminosity of the central source , light echoes propagate into the nebula .
This remarkable phenomenon was the subject of Paper I .
The origin and physical properties of the nebula are however uncertain : it may have been created through mass loss from the star itself , or it could be the remnant of a pre-existing interstellar cloud .

Aims : Our goal is to determine the three-dimensional structure of the light-scattering nebula , and estimate its mass .
This will bring us new clues on the origin of the nebula .
Knowing the geometrical shape of the nebula will also allow us to retrieve the distance of RS Pup in an unambiguous manner using a model of its light echoes ( in a forthcoming work ) .

Methods : The scattering angle of the Cepheid light in the circumstellar nebula can be recovered from its degree of linear polarization .
We thus observed the nebula surrounding RS Pup using the polarimetric imaging mode of the VLT/FORS instrument , and obtained a map of the degree and position angle of linear polarization .

Results : From our FORS observations , we derive a three-dimensional map of the distribution of the dust around RS Pup , whose overall geometry is an irregular and geometrically thin layer .
The nebula does not present a well-defined central symmetry .
Using a simple scattering model , we derive a total dust mass of M _ { \mathrm { dust } } = 2.9 \pm 0.9 M _ { \odot } for the light-scattering dust within 1.8 \arcmin of the Cepheid .
This translates into a total mass of M _ { \mathrm { gas + dust } } = 290 \pm 120 M _ { \odot } , assuming a dust-to-gas ratio of M _ { \mathrm { dust } } / M _ { \mathrm { gas } } = 1.0 \pm 0.3 \% .

Conclusions : The high mass of the dusty nebula excludes that it was created by mass-loss from the star .
However , the thinness of the dust distribution is an indication that the Cepheid participated to the shaping of the nebula , e.g .
through its radiation pressure or stellar wind .
RS Pup therefore appears as a regular long-period Cepheid located in an exceptionally dense interstellar environment .