A complete list of tuples (words) of lengths 1, 2, and 3 over an eight-element anisotropic alphabet of directions

This work, the second preprint of the "Not Just Triangles" research project, introduces and systematically explores the path code (P-code) formalism for the discrete encoding of planar polygonal contours. The P-code is defined as an ordered tuple (word) of direction symbols of length 1, 2, or 3, selected from a specially designed anisotropic alphabet of eight symbols (combining axial (→, ↑, ←, ↓) and sectoral (↗, ↖, ↙, ↘) directions). The study establishes the fundamental concepts of the system, including path canonicalization rules and anisotropic quantization of contour directions. The primary result is a complete combinatorial catalog: a lexicographic enumeration of all 8, 64, and 512 possible single-, double-, and triple-element P-codes, respectively. The core analysis focuses on three-symbol codes (P3-codes), determining the precise conditions under which such a code can correspond to a non-degenerate planar triangle. For each of the 152 realizable triangular P-codes, a concrete geometric example with vertex coordinates is provided. The work demonstrates the P-code's deep connections to various mathematical structures, including algebra (as tuples), graph theory (as Hamiltonian cycles), invariant theory (as a canonical signature), set theory, and mathematical linguistics (as words in a formal language). This formalism establishes a foundational, shift- and scale-invariant language for the symbolic description and classification of geometric shapes based on boundary traversal patterns.