The Snub Cube can be obtained using various methods like paper folding, snubification, physical equilibrium simulation or through the Tribonnaci constant. These methods imply the application of formulas to get the coordinates of the polyhedron. We present a novel method that can be applied directly in any 3D modelling tool, expanding the notion of geometrical construction, without the need for preset formulas or constraints. This can be particularly useful for non-experts like artists, architects, or designers. The method involves deriving the vertices of the polyhedron by intersecting generalized Steinmetz curves. However, to demonstrate the method, we made an analytical development. A similar approach can be applied to the Snub Dodecahedron.