1.  I have a drawsquare method that I call 54 times.  It simply binds a texture to a square.  (And it takes parameters to indicate which picture and which portion (ninth) of the picture I'm using.

2.  Prior to calling drawsquare, I have already glTranslated and glRotated so that my face is where I need to be.

3.  In drawsquare, I glTranslate to the correct ninth, glRotatef to the correct orientation, and paste ONE texture onto ONE square.

4.  When I rotate a side, I set a global angle flag (which I called "a") = -90.  I also set certain flags to certain stickers to indicate that they are to abide by the a.

I have a data structure (which for me is a 3-dimensional array of  pointers) essentially containing 54 flags (and other things I deemed relevant) When I rotate a side I set 21 of these flags to true.  I also have three global ints (sx, sy, sz) to indicate the axis of rotation:  this axis depends on the side I'm rotating.

5.  The rotation stuff just happens as part of the NORMAL EVENT LOOP.  If my angle (a) is anything other than zero, I know that I'm in the middle of animating a side.

In drawsquare, this boils down to one additional line of code:

"if (p->flag) glRotatef (a,sx,sy,sz);"

6.  The stickers are moved "instantly" as soon as I press the key.  BUT since the angle is initially set to -90, the flagged stickers are moved 90 degrees backward before drawing them, i.e. back to their previous location.

Each time the event loop encounters a negative angle, it slightly moves that angle toward zero.