Tessellationa

Tessellationa is a term used in geometry and art to denote the study and practice of tessellations—tilings of a plane or space by shapes that meet edge to edge without gaps or overlaps. The field combines mathematical theory with visual design and appears in both abstract tiling theory and applied disciplines such as computer graphics and architectural ornament.

In tessellationa, researchers examine prototiles, tiling rules, and symmetries. Central concepts include symmetry groups of the plane (wallpaper groups), edge-to-edge tilings, vertex configurations, and the distinction between periodic tilings and aperiodic tilings. The theory extends to three-dimensional space, studying tilings by polyhedra and space-filling arrangements.

Historically, tessellationa draws from Islamic geometric art, mosaics, and the work of mathematicians who developed tiling theory, as well as later explorations of symmetry and aperiodicity, such as Penrose tilings. The plane-wide classification includes regular tilings by a single polygon (such as triangles, squares, and hexagons), semi-regular or Archimedean tilings, and more general uniform tilings.

Applications of tessellationa span design, architecture, crystallography, materials science, and mesh generation in computer graphics. The study also serves educational purposes, offering accessible demonstrations of symmetry, tiling theory, and algorithmic tiling methods.

Note: tessellationa is not a universally standardized term in all literature; in many sources the field is referred to as tiling theory or tessellation theory. This article uses tessellationa as a concise, neutral label for the study and practice of tilings.