Orientations

This is a naming scheme for piece orientations.

We need to precisely describe orientations to describe puzzle solutions.

Axes

The legs of the piece below show the directions of the X, Y, Z axes.

• Positive X goes to the viewer's right.
• Positive Y goes toward the viewer and is the shortest leg.
• Positive Z goes upward and is the longest leg.

Orientation Names

Orientation names have two parts:

• A letter indicating the face that faces down (A,N,E,W,S,U). A means the bottom faces down. N, E, W, S are named after compass directions, where each of these sides face down. U is the upside-down orientation, equivalent to applying the E or W transform twice.
• A digit indicating the number of 90º clockwise turns around the Z axis (0,1,2,3)

Thus, A0 is the identity orientation (no change).

Evaluating Piece Orientations

• Which orientations have overhangs?
• Which orientations are 2D (height=1)?
• What is the footprint of each orientation? (useful for pruning the decision tree when solving)
• Which orientations are duplicates? Which footprints are?