Symmetry in Discrete Geometry

Dear colleagues,

One can briefly describe discrete geometry as the study of discrete arrangements of geometric objects in Euclidean, as well as in non-Euclidean spaces. J. Kepler was the first to raise discrete geometry problems on packings of balls in the early 1610s, but the systematic research began in the late 1940s with the work of L. Fejes Toth. The Hungarian school he founded focused mainly on packing and covering problems, while a number of great mathematicians helped to lay a broad foundation of discrete geometry, including H. S. M. Coxeter, J. H. Conway, B. N. Delaunay, P. Erdos, B. Grunbaum, V. Klee, and C. A. Rogers. Two active areas that have been outstanding from the birth of discrete geometry are sphere packings and tilings. By now, there are a number of equally important research areas of discrete geometry including sphere coverings, periodic and aperiodic tilings, finite subdivision rules, (quasi) crystals, geometric rigidity and flexibility, point-, line-, hyperplane-, and sphere- arrangements, geometric lattices and discrete groups, convex polytopes, regular polytopes and symmetry groups, and geometric graphs. Discrete geometry is centered around problems many of which intend to characterize specific discrete arrangements of geometric objects often with high symmetry. On the other hand, many of the methods used in the study of discrete arrangements are based on a great variety of symmetrizations. Last but not least, regular discrete arrangements are governed by symmetry the study of which is interesting on its own. With the proposed special issue entitled “Symmetry in Discrete Geometry” and to be published in the journal Symmetry we invite the interested researchers to submit survey or research articles on all aspects of symmetry in discrete geometry.

Prof. Karoly Bezdek
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

• Packings
• Coverings
• Arrangements of convex bodies
• Tilings
• Polytopes
• Geometric lattices
• Symmetry groups,
• Discrete convexity
• Extremal discrete geometry