This has been a sometimes fun, but most often infuriating discussion between my wife and I, as well as other family members and friends whenever we bring it up: which side of the bed is the front? Is it the foot end? The side where the heads are? Or are you a rebel and is it the side you get out of bed at?
There is a top and bottom, we know that much for sure. I say the 4 sides are equivalent so the “head” and “foot” depend on how one sleeps. No need to use front and back terminology which is better suited for something you can’t see over or around.
Reminds me of dorsal/ventral, anterior/posterior and rostral/caudal from anatomy. Maybe we need to define an anatomical position for mattresses.
Edit: When standing a mattress up, like during moving, the top and bottom may temporarily be re-designated front and back. Pivot!