[hkgjtwvq] cube deck

create a deck of cards representing the 48 elements of the symmetry group of a cube (isometries of a cube) (automorphism group of a cube).  48 is a good number of cards for a deck, not too difficult to shuffle.

there are two suits, corresponding (roughly) to mirror images.

pairs of cards can be added to yield another: the group action.  how can addition be facilitated to make it easier for humans?  perhaps print the appropriate line of the addition table on the face of each card.  how can be group elements be compactly identified?

describe a group element by a decomposition into rotations of 90 degrees along axes (and zero or one reflection), like Rubik's cube algorithms.  but this is not compact.

an illustration of axis and angle is compact.

augment the deck with d6 dice: two of different colors, mirror images of each other.  how easy is to acquire a d6 die that is the mirror image of the conventional d6 die?

find the card corresponding to a given rotation of a die relative to a canonical unrotated state.  maybe this is the mechanic of games.

or, consider a 60-card deck of just the orientation-preserving symmetries of the regular dodecahedron or icosahedron; 60 is small enough to comfortably shuffle.  previously.  you would only need one d12 (or d20) die.  maybe two, if you want to keep track of before and after a rotation.

do d12 and d20 dice have standardized numbering?

how can one describe a rotation of (say) a dodecahedron?  starting from a canonical orientation, move the face labeled X to the top in a canonical orientation, then orient the X top face to one of 5 possible orientations.  equivalently, top face and "front" face adjacent to top.