This paper presents the development of an all-in-one probe to simultaneously measure all components of the generalized Ohm’s law in reversed-field pinch plasmas and tokamaks. The polyhedral configuration of the Mach probe is achieved through the specific arrangement, angle, and depth of the collimator channel apertures drilled into the surface of a hollow boron nitride cylinder encasing it. This probe includes a central Mach probe to assess the ion velocity field in three dimensions. Initial tests at the RELAX and Madison Symmetric Torus machines have confirmed the probe’s effectiveness, revealing an octahedron form similar to a tetrahedron. The probe seems to function correctly and is expected to facilitate the empirical validation of two-fluid equilibria at the periphery of toroidal plasmas.