wing: the pieces in beween the center edge and corners on a professor
there are 24 wings on a professor, shown below with dark squares
x-center: the corners of the center 3x3
there are 24 x-centers on a professor, shown below with dark squares
+-center: the edges of the center 3x3
there are 24 +-centers on a professor, shown below with dark squares
center edge:
there are 12 center edges on a professor, shown below with dark squares
tredge: a group of 2 matching wings and the matching center