The surface of a three-dimensional topological insulator (TI) hosts surface states whose properties are determined by a Dirac-like equation. The electronic system on the surface of TI nanowires with a polygonal cross-sectional shape adopts the corresponding polygonal shape. In a constant transverse magnetic field, such an electronic system exhibits rich properties because different facets of the polygon experience different values of the magnetic field due to the changing magnetic field projection between facets. We investigate the energy spectrum and transport properties of nanowires, where we consider three different polygonal shapes, all showing distinct properties visible in the energy spectrum and transport properties. Here we propose that the wire conductance can be used to establish the presence of nanowire surface states by rotating the magnetic field and observing a variation in agreement with the cross-sectional shape of the nanowire. Distinguishing between the different shapes also works in the presence of impurities as long as conductance steps are discernible, thus revealing the subband structure.