Orientation

A flat piece

An upright piece

Two weird pieces

Pyramids are said to have one of three orientations:

1. flat
2. upright
3. weird

A flat piece has the lowest of its triangular sides parallel to the playing surface. Some games might care about where the pyramid is pointing or its direction.

An upright piece has its square base parallel to the playing surface, pointing away from the playing surface.

A weird piece is any piece which is neither flat nor upright. Barring psychokinesis or some kind of vortex, a piece needs the help of another piece to be weird.

Note that a piece's orientation has nothing to do with whether or not the piece is grounded.