semiregulär

Semiregulär is a term used in various fields, most notably in geometry and theoretical computer science, to describe objects or concepts that exhibit a degree of regularity but not complete regularity. In geometry, a semiregular polygon is a polygon that has two or more types of regular polygons as faces and is vertex-transitive. This means that all vertices are equivalent under the symmetries of the polygon. Examples include the Archimedean solids, which are semiregular polyhedra.

In a broader mathematical context, semiregularity can refer to structures that possess some, but not all, of the properties of a fully regular structure. For instance, a semiregular graph is a graph that is vertex-transitive and edge-transitive, but not necessarily distance-transitive. This means that any vertex can be mapped to any other vertex by a symmetry of the graph, and any edge can be mapped to any other edge, but not every pair of vertices can be mapped to any other pair of vertices by a symmetry that preserves their distance.

The concept of semiregularity implies a compromise between complete order and complete disorder. It highlights structures that have underlying patterns and symmetries, yet also exhibit variability or a less stringent set of defining properties compared to their fully regular counterparts. This intermediate level of regularity can lead to complex and interesting properties, making semiregular objects subjects of study in various scientific disciplines.