We find that more systematic methods are needed to correlate related orbifolds. We noticed that the color crystallographic groups provide a convenient mechanism for describing group vs. subgroup relationships and wondered what the orbifold for a color group would look like. Thus the antisymmetry elements describe the sheeting character of the two-sheeted cover.
Similar relationships hold for the general color groups.
3-Euclidean crystallographic groups which are called either Shubnikov, Heesch, or magnetic space groups in the crystallographic literature. We would appreciate comments on the approach described and alternate possibilities for correlating orbifolds. Pointers to related ongoing research and literature references would also be appreciated.