Computational Geometry Modeling of a Modular Breeze-Block Design Using Maple: Symmetry, Transformation, and Script Validation

Abstract

This study aims to model, examine, and validate the two-dimensional geometric construction of a modular roster design using Maple. The initial manuscript used the term roaster and interpreted the pattern as a component of a coffee-roasting machine, whereas the configuration of two repeated square modules is more consistent with an architectural roster or breeze block. This study employed a descriptive-computational approach through syntax inventory, coordinate mapping, element measurement, transformation analysis, symmetry examination, and script reproducibility auditing. The results show that the intended model consists of two units measuring 6 × 6 units, centered at (3, 3) and (9, 3). Each unit contains 24 primary points, 24 segments forming six alternating square layers, and 13 circles. The areas of the six polygonal layers form the sequence 36, 18, 9, 4.5, 2.25, and 1.125 square units, with a constant ratio of 1/2. The second unit is obtained through the translation , while each ideal unit exhibits dihedral symmetry . The audit identified several important inconsistencies in the script, including incorrect object terminology, four undefined corner circles in Unit II, two groups of circles omitted from the display command, inconsistent line thicknesses, and a view range that did not explicitly cover both units. After revision, the model consists of 48 primary points, 48 segments, and 26 circles that can be fully visualized. This model is suitable as a basis for parametric design and geometry learning; however, it cannot yet be used to draw conclusions regarding ventilation, lighting, thermal performance, or structural strength before solid-void modeling and physical simulations are conducted.