Semiregulars

Semiregulars is a term used across disciplines to denote systems that exhibit a high degree of regularity but fall short of complete symmetry. The term is most common in geometry and in astronomy, where it designates two distinct classes of objects that share this idea of partial regularity.

In geometry, semiregular polyhedra, also called Archimedean solids, have faces that are regular polygons of more than one type, and the arrangement of faces around each vertex is identical, making the solids vertex-transitive. There are 13 Archimedean solids, including cuboctahedron, icosidodecahedron, rhombicosidodecahedron, and various truncated forms, as well as the two chiral forms known as the snub cube and the snub dodecahedron. In addition to these polyhedra, semiregularity is discussed in the context of uniform tilings, where plane tilings by regular polygons share the same vertex configuration at every vertex.

Semiregular tilings of the plane are uniform tilings by regular polygons with more than one polygon type and the same vertex configuration at every vertex. They include tilings with vertex figures such as 3.12.12 and 4.8.8, among others.

In astronomy, semiregular variables are cool giant or supergiant stars that show periodic or quasi-periodic brightness variations, often with more than one pulsation period. They are less regular than Cepheid variables and vary in character from completely irregular variables. The class is defined by observed light curves and spectral types, and it includes a large population of evolved stars that illuminate aspects of stellar pulsation and late-stage evolution.