Pieces

A gallery of pieces used by puzzles. Each piece is a polycube shape.

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Polycubes are represented as delimited strings of numbers.

numbers represent stacks of cubes (in the z direction, coming out of viewing plane toward viewer)
row of numbers are adjacent stacks (in the x direction, left to right across viewing plane)
single slash / delimits rows (y direction, downward on viewing plane).
double slash // delimits planes (z direction, generally only necessary to represent overhangs)
0s represent empty spaces. Use a 0 in a empty row or plane when there is nothing to represent (for an example, see 'hollow cube' shape). This prevents two / delimiters from being mistaken for a single // delimiter.

Every polycube gets a shorthand name.

Name rods by length, prefixed with "I" ("I4")
Name rectangular solids by their dimensions, delimited with "x" ("1x2x3")
When possible, name 2D polycubes by a letter approximating their shape ("P")
When possible, name polycubes by overhang-free faces, with bigger faces first ("PQO")
Use + to indicate a shape where footprint has been extended, generally along the Z axis ("PLR+")
Use +N to indicate a shape where an N-long spike has been added, generally at the top left along the Z axis ("L+3", "knot+1")

Compact notation implies a default orientation. Best practices for choosing an orientation:

Favor orientations that are easy to quickly assess and understand.
Minimize the number, size, and complexity of z-axis structures extruding from the xy plane. If there is a complex 2D shape, lay it out flat on the xy plane so the viewer can see it easily.
Don't worry about finding a canonical/minimal representation that can be algorithmically determined (eg, shortest or lexicographically earliest representation). Instead, orient in a way that is convenient/intuitive.
If the name of a polycube uses letters to describe its shape, try to match orientation and chirality of those letters. (TODO: match chirality? of footprint or piece when viewed head-on?)