A directed tree of 24 triangle types

This study is devoted to a comprehensive analysis of a hierarchical graph model for the classication of planar non-degenerate triangles. The model is represented as a directed rooted tree that visualizes the relationships between geometric classes. The paper carries out a detailed investigation of the graph structure, including the count of nodes (41), edges (40), and hierarchy levels (4). A total of 24 equivalence classes (paths from the root to the leaves) were identied, distributed unevenly across the three main branches, indicating dierent degrees of variability within the triangle types. An analysis of signicant subgraphs conrmed the tree-like nature of the model and revealed key star-shaped branching patterns. The results demonstrate the eectiveness of the proposed graph as a rigorous tool for taxonomy and provide a foundation for its use in computational geometry. Bilingual Publication Structure: This work is presented in a bilingual format (English/Russian), offering complete parallel texts of the abstract, introduction, core methodology, results, and conclusions. This approach ensures broad accessibility and facilitates dissemination within the international community as well as among Russian-speaking researchers.