Cisgeometria

Cisgeometria is a term that appears in some mathematical discussions to denote a prospective branch of geometry focusing on cis configurations—geometric relations defined relative to a fixed orientation, such as a reference plane or axis. In this approach, elements are partitioned into cis-classes depending on their relative position with respect to the reference, and the central objective is to study properties and invariants that remain under transformations preserving this cis relation.

Key objects in cisgeometria include cis-polytopes and cis-manifolds, which are defined by constraints that depend on the side or orientation of components with respect to the reference. The theory seeks to understand how classic geometric notions such as distance, angle, and curvature interact with the cis partition, and how cis-congruence differs from ordinary congruence or similarity.

The mathematical framework can draw on tools from symmetry, group theory, and topology, as well as computational geometry for visualization. Typical problems involve classifying configurations up to cis-congruence and constructing canonical representations that respect the cis relation.

Status: Cisgeometria is not a widely established field in mainstream mathematics, but it has appeared in informal discussions and exploratory papers. It is presented as a conceptual lens for exploring orientation-based constraints in geometry and may intersect with studies of symmetry, oriented geometry, and geometric topology.

Further reading can be found in general discussions of symmetry and orientation in geometry, and in works that examine geometry under alternative equivalence relations.