Strange Cube Index 

The possible faces will have between 6 and 10 pieces, with a maximum of 6 kites and 8 triangles, and the constraint 2 × NK + NT = 12, NK = (12 − NT) / 2.
I will identify unique faces by converting the triangles and kites to binary (kites being '1' and the triangles '0') and using this to generate a key. As rotating a face doesn't really change it, I will find the rotation that generates the largest key. In the following images the keys are this binary number and the pieces are represented by ones and twos, so that the sum is always 12.
The list below shows all the possible arrangements of the pieces, there is no guarantee that all of these can be reached using the possible transformations of the cube, but the transformations page suggests that they can.
(c) John Whitehouse 2017