poligonokra

Poligonokra is a term used in geometry and digital art to describe a family of polygon-based figures and tilings defined by recursive subdivision and heterogeneous polygon counts. The concept emphasizes combining polygons of different shapes within a single connected mosaic, often arranged to cover a plane without gaps.

Etymology and usage: The name blends polygon-related terminology with a suffix that signals a category or class. It has gained traction in discussions of algorithmic tiling and computational design, where artists and researchers explore dynamic, self-similar patterns and the interplay between local rules and global structure.

Structure and rules: A poligonokra tiling permits polygons of varying n-gon shapes meeting edge-to-edge. Local rules govern vertex configurations, edge adjacency, and subdivision methods. Some variants allow curved boundaries as a generalization, yielding smooth transitions between polygonal regions while preserving a cohesive overall pattern.

Construction methods: Poligonokra patterns are typically generated by recursive subdivision of base polygons or by applying a tiling rule across a plane, producing self-similar and, in some cases, quasi-periodic mosaics. Transformations such as scaling, rotation, and reflection generate families of related patterns.

Examples and variants: Common forms include mixtures of triangles, quadrilaterals, and hexagons, arranged in both periodic and nonperiodic layouts. Quasi-periodic examples resemble Penrose tilings in their avoidance of translational symmetry while maintaining local regularity.

Applications and significance: The concept informs computer graphics, architectural tiling, mathematical visualization, and art education, offering a framework for exploring polygonal diversity within cohesive mosaics.

See also: polygon tiling, tessellation, polyform, quasi-periodic tiling.