Strange Cube Index 

Once you have made a few rotations the "cube" is unlikely to remain cubic, but for want of a better name I'm going to refer to them as cubes anyway. A cube will always have 8 triangles and 8 kites, so we can use the previous list of faces to generate the set of potential cubes.
Whether all of the cubes can actually be realised will be explored on the transformations page.
To identify the cubes I have labelled them with the keys that define the faces. As turning the cube upside down isn't really a transformation I've only shown those cubes where the top face's key is greater than or equal to the botom one's.
(c) John Whitehouse 2017