Lying is actually two different postures according to B325 and B364:
- lying prone (face down)
- lying face up
The latter could also be referred to as lying supine although GURPS doesn't use the term "supine" here in early books until Douglas Cole smartly uses it on page 10 of GURPS Martial Arts: Technical Grappling
TG37 also uses the superfluous phrase "lying down" on pg 37, perhaps to emphasize its relation to an inferior surface.
Ken Clary in Pyramid 3/34 pg 11 "A New Take On Grappling" proposed in a blue box on the lower left Posture, Orientation, and Facing:
- There is one new posture: A character can lie on his side, which is halfway between lying prone (face down) and lying face up, sharing their posture penalties.
This idea unfortunately doesn't appear to have made it into Technical Grappling. It could've been further defined as:
- Lying Left
- Lying Right
Perhaps some of the difficulty in adapting that would be the hexagonal nature and determining which direction the gaze would be in, since that could be either gazing upward (away from hex legs are in) or downward (towards hex legs are in).
Clary defines Orientation:
- the direction your body is pointing,
- that is,
- which hex side your head points toward
He also defines relative orientation:
- relative orientation is how this compares to your opponent’s orientation:
- whether you are pointed in the same direction,
- to the side of each other,
- in opposite directions,
- etc.
The last point is because you might not be pointing to the "side" if you aren't pointing the same/opposite. For example: if pointing to one of the 3 forward hexes but not the exact 60 degree orientation of the other.