Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.9
2.7
Journals
Symmetry
Special Issues
Mathematical Crystallography 2019
share announcement

Mathematical Crystallography 2019

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 August 2019) | Viewed by 4878

Special Issue Editor

Prof. Sergey V. Krivovichev

E-Mail Website
Guest Editor
Department of crystallography, Institute of Earth Sciences, Saint-Petersburg State University, 199155 Saint-Petersburg, Russia
Interests: mineralogy; crystallography; complexity; crystal chemistry; nuclear chemistry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Despite the enormous success of experimental crystallography achieved in the 20th century, the very problem of the emergence of order and symmetry in discrete structures is far from being completely understood. This Special Issue invites contributions on various mathematical aspects of modern crystallography, starting from diffraction theory and disorder and ending at deeply mathematical problems of symmetry, sphere packings, polyhedra and discrete point sets.

Prof. Sergey V. Krivovichev
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.

Keywords

  • crystals
  • crystal structure
  • symmetry
  • long-range order
  • sphere packings
  • discrete point systems
  • polyhedral arrangements
  • lattices
  • space groups
  • quasicrystals

Published Papers (1 paper)

Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

18 pages, 6168 KiB  
Article
Prototiles and Tilings from Voronoi and Delone Cells of the Root Lattice An
by Nazife Ozdes Koca, Abeer Al-Siyabi, Mehmet Koca and Ramazan Koc
Symmetry 2019, 11(9), 1082; https://doi.org/10.3390/sym11091082 - 28 Aug 2019
Cited by 4 | Viewed by 4517
Abstract
The orthogonal projections of the Voronoi and Delone cells of root lattice A n onto the Coxeter plane display various rhombic and triangular prototiles including thick and thin rhombi of Penrose, Amman–Beenker tiles, Robinson triangles, and Danzer triangles to name a few. We [...] Read more.
The orthogonal projections of the Voronoi and Delone cells of root lattice A n onto the Coxeter plane display various rhombic and triangular prototiles including thick and thin rhombi of Penrose, Amman–Beenker tiles, Robinson triangles, and Danzer triangles to name a few. We point out that the symmetries representing the dihedral subgroup of order 2 h involving the Coxeter element of order h = n + 1 of the Coxeter–Weyl group a n play a crucial role for h -fold symmetric tilings of the Coxeter plane. After setting the general scheme we give samples of patches with 4-, 5-, 6-, 7-, 8-, and 12-fold symmetries. The face centered cubic (f.c.c.) lattice described by the root lattice A 3 , whose Wigner–Seitz cell is the rhombic dodecahedron projects, as expected, onto a square lattice with an h = 4 -fold symmetry. Full article
(This article belongs to the Special Issue Mathematical Crystallography 2019)
►▼ Show Figures

Graphical abstract

Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-1
Back to TopTop