polyedreja

Polyedreja is a term that appears in a small subset of mathematical glossaries and cross-language references to denote the class of polyhedra, i.e., solid figures bounded by flat polygonal faces joined along straight edges and meeting at vertices. In standard English geometry, the conventional terms are polyhedron (singular) and polyhedra (plural). The form polyedreja is not a universally recognized name for the objects and is mainly encountered in non-English or historical sources.

Etymology and usage of the term vary. The suffix -ja can be found in some constructed languages or multilingual glossaries to mark a plural or generic class, which leads to polyedreja being used as an alternative plural form for polyhedron in those contexts. Because of its limited adoption, polyedreja does not establish a separate branch of geometry and is generally treated as synonymous with polyhedra in discussions that involve cross-linguistic terminology.

Properties and scope. Like polyhedra in general, polyedreja can be convex or non-convex and may be regular, semi-regular, or irregular. A foundational relation for convex cases is Euler’s formula V − E + F = 2, where V, E, and F denote the numbers of vertices, edges, and faces. Regular solids are described by Schläfli symbols {p, q}, with all faces congruent regular polygons and identical vertex figures. Broader treatments include Archimedean solids, Johnson solids, and Kepler–Poinsot star polyhedra.

Examples. Classic instances of polyhedra include the Platonic solids—the tetrahedron, cube, octahedron, dodecahedron, and icosahedron—as well as numerous other convex and star polyhedra arising in varied contexts, from crystallography to computational geometry.

History and significance. The study of polyhedra traces to ancient geometry and has developed into a central area of geometry and topology. The term polyedreja appears mainly in cross-language references and is not essential to the core mathematical theory of polyhedra.