Piece types¶
How to name piece types for an HSC2 puzzle.
Warning
This is a draft
In general, piece types should be based on ther geometric layout, rather than being based on a particular solution method or solving order. This system was chosen so the piece names are neutral relative to the solution.
A piece that is at the center of the puzzle should be called a core. However, if this piece is not fixed, like in the <Rw, Uw> 3×3, it can have another name, such as anticore. A piece that is at the center of a facet of the puzzle should be called a center. A piece that is at the center of another element of the puzzle should be named after that element, i.e. corner, edge, or ridge, as in the 3n.
A piece that is not at the center of an element of the puzzle lies between the centers of some nearby elements that are all incident. The piece should be in the top-level group named after a piece centered at the highest-rank element of that subflag. That name should be prefixed by letters corresponding to the other elements of the subflag by increasing rank, where corner is V, edge is E, and ridge is R, except that a V-edge is called a wing. In 3 dimensions, V-center is replaced by X-center and E-center is replaced by T-center. If the subflag is a flag, it is called an oblique. Obliques can have two chiralities that depend on the sign of the determinant of the matrix whose rows are the centers of the elements by increasing rank: if it is positive, the piece is an oblique (right), and otherwise it is an oblique (left).
If multiple pieces have the same name, they should be disambiguated with adjectives. These can include inner and outer (as in the elite pentultimate's X-centers), pentagonal and hexagonal (as in the Tuttminx), big and small, or numbers (as in large N3 puzzles).
If an orbit of indistinguishable pieces occupies multiple positions, it can be given a name from outside of this system (as in the bagua cube's triangles, which can be both X-centers and T-centers). Exceptions can be made to this system for sufficiently compelling reasons, such as shapemods where the outer geometry does not match the axis system (like the hexaminx), or puzzles with established piece names (such as the face-turning octahedron's triangles).