On2s

On2s is a term used in speculative and educational contexts to denote a family of two-dimensional structures. It is not tied to a single object but rather to a collection of models that share a focus on two-dimensionality and symmetry. In discussions across mathematics, computer graphics, and design, On2s serve as a convenient umbrella for exploring how local two-dimensional rules translate into broader global forms.

The name combines a reference to two-dimensionality with an open-ended use of the symbol On, which in this context functions as a flexible marker for symmetry groups or transformation sets. Because On2s are defined by context rather than a fixed formalism, different authors may attach slightly different technical meanings depending on the domain and educational goal.

Commonly, On2s are described as spaces or surfaces that locally resemble a plane but can exhibit varying global topologies, such as holes or boundaries. They are typically represented in digital work as meshes, grids, or parametric surfaces, which makes them useful for visualizing concepts in topology, geometry, and conformal mappings. In programming and graphics, On2s provide a framework for texture mapping, surface parameterization, and mesh processing.

Applications of On2s are largely didactic and design-oriented. They appear in textbook explanations of two-dimensional manifolds, in interactive geometry software to illustrate curvature and tessellation, and in art and game design as a conceptual toolkit for constructing visually coherent 2D worlds. See also 2D manifolds, topology, and symmetry groups.