Context. The penumbra of sunspots has a complex magnetic field topology whose three-dimensional organization remains unclear after more than a century of investigation. Aims: I derive a geometrical model of the penumbral magnetic field topology from an uncombed inversion setup designed to reproduce the net circular polarization (NCP) of simultaneous spectra in near-infrared (IR; 1.56 μm) and visible (VIS; 630 nm) spectral lines. Methods: I inverted the co-spatial spectra of five photospheric lines with a model that mimicked vertically interlaced magnetic fields with two distinct components, labeled background field and flow channels because of their characteristic properties (flow velocity, field inclination). The flow channels were modeled as a perturbation of the constant background field with a Gaussian shape using the SIRGAUS code. The location and extension of the Gaussian perturbation in the optical depth scale retrieved by the inversion code were then converted to a geometrical height scale. By estimating the geometrical size of the flow channels, I investigated the relative amount of magnetic flux in the flow channels and the background field atmosphere. Results: The uncombed model is able to reproduce the NCP well on the limb side of the spot and less successfully on the center side; the VIS lines are better reproduced than the near-IR lines. I find that the Evershed flow happens along nearly horizontal field lines close to the solar surface given by optical depth unity. The magnetic flux that is related to the flow channels constitutes about 20-50% of the total magnetic flux in the penumbra. Conclusions: The gradients that can be produced by a Gaussian perturbation are too small for a perfect reproduction of the NCP in the IR lines with their small formation height range, where a step function seems to be required. Two peculiarities of the observed NCP, a sign change in the NCP of the VIS lines on the center side and a ring structure around the umbra with opposite signs of the NCP in the Ti I line at 630.37 nm and the Fe I line at 1565.2 nm, deserve closer attention in future modeling attempts. The large fraction of magnetic flux related to the flow channel component could suffice to replenish the penumbral radiative losses in the flux tube picture. Appendices A and B are only available in electronic form at http://www.aanda.org