__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