Alternate direction systems for spatial reference

All answers so far assume a system of orthogonal directions, each having an "anti direction". I suspect this predisposition is connected to our left-right symmetric bodies with natural forwards and backwards, as well as ups and downs. Languages constructed for aliens need not conform to this!

Take a starfish, for instance. If they have five distinct arms, that would give five directions in their plane, along with up and down.

For radially symmetric, disk-shaped creatures (or for communicating between radially symmetric spaceships or other vehicles) the only meaningful purely self-relative directions would likely be relative up and relative down (along with hither and away). For a creature shaped like a jellyfish, without any visual clues to other fixed directions, this could be combined with cardinal up and down.

Star or disk shaped creatures could of course point, either by turning their up or down towards something (which would be two different prepositions!), or by deforming themselves, shining a light etc. They could also use auxiliary phrases as "towards Alice" or "the way we came".

A more sophisticated option would also be to talk of the direction perpendicular to cardinal up AND to relative up, maybe like a cross product in mathematics? This would be sort of akin to our left and right, if the creature moves in its relative up direction, that is.

Okay. How about instead of an egocentric direction system, employing a listener-centric or "you"-centric system? We do this in natural language when we say "On your left" or "At your 3:00". Probably such a system would be developed among speakers from a highly empathetic and listener-oriented culture, where the individual's reference is considered secondary to the listener's.

For directions on a galactic scale, much SF (and the Traveller RPG) use Coreward (toward the center of the galaxy), Rimward (away from the center of the galaxy), Spinward (moving about the center of the galaxy in the same direction as general stellar motion), and Antispinward or Trailing (moving about the center of the galaxy in the direction opposite to the general stellar motion).

So, one idea I was considering is a spatial reference system designed for indoor navigation. It's intended to coexist alongside an egocentric direction system which is much more typical.

There's a cardinal direction, let's call it P that refers to the direction towards the primary entrance/exit or "downhill" as a metaphorical extension.

If used in a room or house, the primary entrance is the front door to the house, the main door to the room, the door you used, or the door that is currently to your back.

If used outside on a hill or mountain, the foot of the hill is the primary entrance. Let q refer to a direction 90 degrees to the right of the current direction.

The idea, basically, is that if you are travelling uphill or into a room, P is the direction you would have to go to double back.

Here's a crude drawing of a room with the directions labeled with their symbolic names.

    +-------------------------------------+
    |                                     |
    |                                     |
    |                                     |
    |                                     |
    A                 Pq                  |
                       |                  |
                   P---+---Pqq            |
                       |                  |
    V                 Pqqq                |
    |                                     |
    |                                     |
    |                                     |
    +-------------------------------------+