With this customizer you can generate all of the isogonal (vertices are equivalent) truncations of a cube that have mirror symmetry. This includes both the convex and non-convex possibilities. The convex uniform (isogonal with regular polygons) examples are predefined, and can be selected from a list. I am still in the process of making the definitions of all of the non-convex examples. If you choose the "arbitrary isogonal" option then also select the "Isogonal" tab to set the spherical coordinates of the generating vertex. All of the other vertices are calculated from the first one.