I'm wondering if it is possible for a planet to have one pole always facing its star, the other always facing away (by rotating as if a tidal-locked planet), but style have a day and night cycle on some part of it (by having another axis of rotation ?).
In case I'm not clear enough, I drew this wonderful paint schema to illustrate :
Is it possible for a planet to rotate in a way that would allow this ?
Would there be another natural way to achieve the same result outside of the rotation ?