Various types of structures, composed of several copies of the same or similar building blocks have been studied for many years by many communities of scholars in various branches of mathematics and in other sciences. Examples of such structures are: polyhedra, polytopes, polycubes, polycirculants, polyominoes, polyhexes, polymers, tesselations, arrangements of points and lines, configurations of points and circles, etc. However, although they have the same common characteristics (composability ftom smaller »atoms«), there has been no attempt as yet to study such structures from a unified point of view.

This special issue aims at initiating a general theory of polystructures, as well as stimulating the interest in their relevance and importance in applications as perfect mathematical models of various phenomena in natural and social sciences, Its goal is to identify the main problems related to various polystructures (e.g. the problems of:enumeration, classification, coding and finding the »best« members of a certain family of such structures – in the sense that they represent the optimal solution to some extremal problem), to compare different methods for solving these problems (e.g. using various quotient objects and related covering constructions as in topological graph theory; studying various indices; introducing various conditions with forbidden substructures as in graph theory; etc.), and to derive as much results as possible from the same general theoretical (axiomatic) framework, introducing the key concepts (e.g. the whole and its building blocks, symmetry, fundamental domain of a polystructure, etc). Identifying such concepts, problems, methods, and focusing on their similarities may encourage the transfer of results related to them from different research fields, initiate new research topics related to various polystructures and eventually lead to a unified theory of polystructures. Since many objects in nature and society are composed of the same or similar small parts, various polystructures may serve as mathematical models of their shape, composition, movement and function. Scholars may be interested to discover and explain how different types of polystructures serve as mathematical models of various natural and social phenomena.

The following types of articles are expected for this special issue (although this is not an exclusive list):

Research articles from a certain special field of research (e.g. theory of polytopes, theory of configurations of points and lines, etc.) may focus on problems of enumeration, classification and coding of the members of a certain family of polystructures (e.g. coding of polyhexes with cyclical sequences of numbers in mathematical chemistry); they may also study their symmetries (or even more general automorphisms) and show how to reduce them to their quotient objects (e.g. fundamental domains in the theory of uniform polyhedra), or, conversely, to reconstruct them from these quotients (e.g. using voltage graphs in topological graph theory); they may ascribe to them various quantitative indices to measure their various properties and qualities (e.g. the optimal distribution of their parts in space); they may search for the “best” objects in a certain family of polystructures (in the sense that they represent the optimal solution to some extremal problem), or try to characterize those without certain forbidden substructures (e.g. forbidden minors in graph theory); they may try to develop effective codes for succinctly expressing various shapes and functions of various (static or changing or growing) polystructures in nature, or present some other application of polystructures in biology, mathematical chemistry, ecology, etc.

Review articles may either focus on reviewing concepts, problems, methods and results related to certain family of polystructures (e.g. regular polygonal structures) from various papers, or on comparing two or more families of polystructures in the same way.

Theory-building articles may try to identify the concepts, problems and methods, related to polystructures in general, thus contributing to the realization of the goal of building a useful and wide applicable general theory of polystructures.