Polyhedral Structures

Dear Colleagues,

Since ancient times, mathematicians and scientists have been studying the geometry of polyhedra and polyhedral structures in ordinary Euclidean space. With the passage of time, various notions of polyhedra have attracted attention and have brought to light new exciting classes of symmetric structures, including the well-known Platonic and Archimedean solids, the Kepler-Poinsot star polyhedra, the Petrie-Coxeter polyhedra, and the Grünbaum-Dress polyhedra, as well as the more recently discovered chiral skeletal polyhedra and regular polygonal complexes. Over time we can observe a shift from the classical approach of viewing a polyhedron as a solid, to topological and algebraic approaches focussing on the underlying maps on surfaces, to graph-theoretical approaches highlighting the combinatorial incidence structures and featuring a polyhedron as a skeletal figure in space.

This Special Issue of Symmetry features articles about polyhedral structures, with symmetry as the unifying theme. We are soliciting contributions covering a broad range of topics including:  convex and non-convex polyhedra and higher-dimensional polytopes in spherical, euclidean, hyperbolic, or other spaces; skeletal polyhedral structures and their graphs; maps and polyhedra on surfaces of higher genus; abstract polyhedra and polytopes; polytopes, symmetry groups, and reflection groups; classification of polytopes by transitivity properties of symmetry groups; regular, chiral, and Archimedean polyhedra and polytopes; various classes of highly-symmetric polyhedra, such as vertex-, edge, or face-transitive polyhedra, regular-faced polyhedra, and equivelar maps or polyhedra; tessellations and space-fillers; polyhedra and crystallography; polyhedra in nature; polyhedra in art, design, ornament, and architecture; polyhedral models; and polyhedral design. 

Prof. Dr. Egon Schulte
Guest Editor

Manuscript Submission Information

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