Polygrids

Polygrids represent a class of two-dimensional discrete structures. They are formed by the interconnection of polygonal cells arranged in a repeating pattern. Unlike traditional grid systems that are typically rectangular or hexagonal, polygrids can incorporate a wider variety of polygon shapes and arrangements, allowing for greater flexibility in design and application. The fundamental characteristic of a polygrid is its tessellation property, where the polygons fit together without any gaps or overlaps.

The specific arrangement and types of polygons used in a polygrid dictate its overall properties. For instance, a polygrid composed of triangles will exhibit different structural behaviors and aesthetic qualities compared to one made of pentagons or a mix of shapes. This adaptability makes polygrids suitable for various fields. In architecture and design, they can be used for creating complex facades, structural elements, or decorative patterns. In computer graphics and simulation, polygrids offer alternative meshing strategies for representing surfaces and volumes, potentially improving computational efficiency or accuracy for specific problem domains. Research into polygrids often focuses on their geometric properties, mathematical descriptors, and potential applications where their unique tessellation and structural characteristics can be leveraged.