Rhombic faces have 5 positions within octahedral symmetry.
There are two topological types, with the same number of elements, the same symmetry, but having a somewhat different arrangement of rhombic faces.
[1] The type T has 8 rhombi meeting at the center positions of a cube's 6 faces.
3 meet at the 8 corners of a cube.
[3] Type C is a 12-zone zonohedrification of a truncated cube.