Discrete Hexagonal–Triangular Network Generated by a Quadratic Polynomial

This example demonstrates how to build a discrete geometric network on hexagonal and triangular lattices by evaluating and using a degree-2 (quadratic) polynomial to drive point placement and polygon/edge connectivity. The key math concepts include quadratic functions (discrete polynomial values on lattice points), geometric transformations and similarity mapping to reuse local patterns across the lattice, and the iterative/discrete nature of construction via sequences. In GeoGebra, the construction is reflected by using Sequence to generate parameter/index lists (e.g., n, u, t1, A, T, B), Polygon to assemble lattice-based polygonal network components (e.g., poly1, L_1, L_2, L_3), and Flatten to transform nested structures of points/segments into a drawable form (e.g., flT, flH, fpT, fpH). Suitable for advanced high school through introductory university topics such as discrete geometry visualization, function-driven construction, and understanding how transformations affect repeated geometric patterns.