Special Issue "Rigidity and Symmetry"


A special issue of Symmetry (ISSN 2073-8994).

Deadline for manuscript submissions: closed (31 March 2015)

Special Issue Editor

Guest Editor
Dr. Bernd Schulze
Department of Mathematics and Statistics, Fylde College, Lancaster University, Lancaster, LA1 4YF, UK
Website: http://www.maths.lancs.ac.uk/~schulzeb/
E-Mail: b.schulze@lancaster.ac.uk
Interests: discrete geometry; rigidity theory; symmetry; triangulations; polytope theory; graph theory; matroids; combinatorics; algebraic methods; representation theory; computational geometry; interdisciplinarity; rigidity and flexibility of symmetric framework systems; “equal-area-triangulation problems”

Special Issue Information

Dear Colleagues,

The mathematical theory of “rigidity” investigates the rigidity and flexibility of structures which are defined by geometric constraints (fixed lengths, fixed areas, fixed directions, etc.) on a set of rigid objects (points, lines, polygons, etc.). This theory has both combinatorial and geometric aspects and draws on techniques from a wide range of mathematical areas, including graph theory, matroid theory, positive semidefinite programming, representation theory of symmetry groups, algebraic and projective geometry, and even operator theory.
Since the rigidity and flexibility properties of a structure—either man-made, such as a building, bridge or mechanical linkage, or found in nature, such as a biomolecule, protein or crystal—are critical to its form, behavior and functioning, rigidity theory has many practical applications in fields such as engineering, robotics, computer-aided design, materials science, medicine and biochemistry.
Since symmetry appears widely in both natural and man-made structures, the study of structures with additional symmetry—both finite structures with point group symmetry and infinite structures with periodic or crystallographic symmetry—is an important area of research which has seen a dramatic increase in interest over the last few years, both in mathematics and in the applied sciences.
The aim of this special issue of “Symmetry” is to present a broad spectrum of the latest developments and current research concerning the rigidity and flexibility of symmetric geometric constraint systems, and to foster the exchange of ideas among workers who focus on different aspects and applications of the field.

Dr. Bernd Schulze
Guest Editor


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. Papers will be published continuously (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as 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 refereed through a 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 quarterly 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 800 CHF (Swiss Francs).


  • rigidity of frameworks
  • geometric constraint systems
  • flexibility
  • mechanisms
  • linkages
  • symmetric frameworks
  • point group symmetry
  • periodic frameworks
  • crystallographic symmetry
  • molecular structures
  • pebble game algorithms
  • gain graphs
  • packings

Published Papers (5 papers)

Download All Papers
Sort by:
Display options:
Select articles Export citation of selected articles as:
Select/unselect all
Displaying article 1-5
p. 774-787
Symmetry 2015, 7(2), 774-787; doi:10.3390/sym7020774
Received: 3 April 2015 / Revised: 19 May 2015 / Accepted: 19 May 2015 / Published: 27 May 2015
Show/Hide Abstract | PDF Full-text (2606 KB)
(This article belongs to the Special Issue Rigidity and Symmetry)
p. 954-974
Symmetry 2014, 6(4), 954-974; doi:10.3390/sym6040954
Received: 3 October 2014 / Revised: 27 October 2014 / Accepted: 6 November 2014 / Published: 18 November 2014
Show/Hide Abstract | PDF Full-text (460 KB) | HTML Full-text | XML Full-text | Supplementary Files
(This article belongs to the Special Issue Rigidity and Symmetry)
p. 516-550
by , ,  and
Symmetry 2014, 6(3), 516-550; doi:10.3390/sym6030516
Received: 31 March 2014 / Revised: 5 June 2014 / Accepted: 12 June 2014 / Published: 27 June 2014
Show/Hide Abstract | PDF Full-text (1266 KB) | HTML Full-text | XML Full-text | Supplementary Files
(This article belongs to the Special Issue Rigidity and Symmetry)
p. 368-382
by ,  and
Symmetry 2014, 6(2), 368-382; doi:10.3390/sym6020368
Received: 15 January 2014 / Revised: 15 April 2014 / Accepted: 4 May 2014 / Published: 15 May 2014
Show/Hide Abstract | PDF Full-text (290 KB) | HTML Full-text | XML Full-text
(This article belongs to the Special Issue Rigidity and Symmetry)
p. 308-328
by ,  and
Symmetry 2014, 6(2), 308-328; doi:10.3390/sym6020308
Received: 25 February 2014 / Revised: 11 April 2014 / Accepted: 15 April 2014 / Published: 24 April 2014
Show/Hide Abstract | PDF Full-text (617 KB) | HTML Full-text | XML Full-text
(This article belongs to the Special Issue Rigidity and Symmetry)
Select/unselect all
Displaying article 1-5
Select articles Export citation of selected articles as:

Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Characterization of Network Rigidity Using Eigenmode Analysis
uthors: Youngho Park and Sangil Hyun
Nano IT Materials Lab, Korea Institute of Ceramic Engineering and Technology, Seoul 153-782, Korea
The eigenmode analysis was employed to investigate the rigidity of various networks determined by certain conditions on zero frequency modes. We introduced the analysis to identify structural characterization of two-dimensional regular networks and also irregular networks. The analysis was shown reliable to determine the global network rigidity, and can also identify local floppy regions in the mixture of rigid and floppy regions. It is useful to determine the structural characteristics of general networks which the traditional Maxwell counting scheme based on the statistics of nodes (degrees of freedom) and bonds (constraints) cannot usually determine. The eigenmode analysis is under development for various practical applications on more general network structures in three dimensions.

Last update: 14 November 2014

Symmetry EISSN 2073-8994 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert