...the way sprites are handled allows two rotations to be compacted into one sprite. The one sprite, which is drawn to depict only one rotation by itself, is merely flipped to serve as a depiction for the second rotation...If you take a look at a typical character WAD, you'll see listings that consist of lumpnames like these:
PLAYA1
PLAYA2A8
PLAYA3A7
PLAYA4A6
PLAYA5
Note how some of the frames define two rotations: PLAYA2A8, for example, defines that it can be used for rotations "A2" and "A8"...
...Note, however, that because the game flips the one sprite using this naming scheme, asymmetrical features would be flipped as well. For example, if the character carried a weapon on their right hand, it would also appear on their left hand by error when the game flips the sprite, as if they were "switching hands". This can be seen as problematic...
...This way, different sprites can be drawn for all the rotations. PLAYA2 would show the character holding their weapon on their right hand — the one away from the camera, while PLAYA8 could still show the character holding their weapon on their right hand — in this case, the one towards the camera.