Next Issue
Volume 4, September
Previous Issue
Volume 4, March
 
 

Symmetry, Volume 4, Issue 2 (June 2012) – 5 articles , Pages 265-335

  • Issues are regarded as officially published after their release is announced to the table of contents alert mailing list.
  • You may sign up for e-mail alerts to receive table of contents of newly released issues.
  • PDF is the official format for papers published in both, html and pdf forms. To view the papers in pdf format, click on the "PDF Full-text" link, and use the free Adobe Reader to open them.
Order results
Result details
Section
Select all
Export citation of selected articles as:

Research

262 KiB  
Article
Maniplexes: Part 1: Maps, Polytopes, Symmetry and Operators
by Steve Wilson
Symmetry 2012, 4(2), 265-275; https://doi.org/10.3390/sym4020265 - 16 Apr 2012
Cited by 17 | Viewed by 5046
Abstract
This paper introduces the idea of a maniplex, a common generalization of map and of polytope. The paper then discusses operators, orientability, symmetry and the action of the symmetry group. Full article
(This article belongs to the Special Issue Polyhedra)
Show Figures

Figure 1

325 KiB  
Article
Following Knots down Their Energy Gradients
by Louis H. Kauffman
Symmetry 2012, 4(2), 276-284; https://doi.org/10.3390/sym4020276 - 27 Apr 2012
Cited by 3 | Viewed by 6196
Abstract
This paper details a series of experiments in searching for minimal energy configurations for knots and links using the computer program KnotPlot. Full article
(This article belongs to the Special Issue Symmetry and Beauty of Knots)
Show Figures

Figure 1

30730 KiB  
Article
Diagrammatics in Art and Mathematics
by Radmila Sazdanovic
Symmetry 2012, 4(2), 285-301; https://doi.org/10.3390/sym4020285 - 22 May 2012
Cited by 2 | Viewed by 8107
Abstract
This paper explores two-way relations between visualizations in mathematics and mathematical art, as well as art in general. A collection of vignettes illustrates connection points, including visualizing higher dimensions, tessellations, knots and links, plotting zeros of polynomials, and new and rapidly developing mathematical [...] Read more.
This paper explores two-way relations between visualizations in mathematics and mathematical art, as well as art in general. A collection of vignettes illustrates connection points, including visualizing higher dimensions, tessellations, knots and links, plotting zeros of polynomials, and new and rapidly developing mathematical discipline, diagrammatic categorification. Full article
(This article belongs to the Special Issue Symmetry and Beauty of Knots)
Show Figures

Graphical abstract

5009 KiB  
Article
Knots in Art
by Slavik Jablan, Ljiljana Radović, Radmila Sazdanović and Ana Zeković
Symmetry 2012, 4(2), 302-328; https://doi.org/10.3390/sym4020302 - 05 Jun 2012
Cited by 3 | Viewed by 11879
Abstract
We analyze applications of knots and links in the Ancient art, beginning from Babylonian, Egyptian, Greek, Byzantine and Celtic art. Construction methods used in art are analyzed on the examples of Celtic art and ethnical art of Tchokwe people from Angola or Tamil [...] Read more.
We analyze applications of knots and links in the Ancient art, beginning from Babylonian, Egyptian, Greek, Byzantine and Celtic art. Construction methods used in art are analyzed on the examples of Celtic art and ethnical art of Tchokwe people from Angola or Tamil art, where knots are constructed as mirror-curves. We propose different methods for generating knots and links based on geometric polyhedra, suitable for applications in architecture and sculpture. Full article
(This article belongs to the Special Issue Symmetry and Beauty of Knots)
Show Figures

Figure 1

177 KiB  
Article
Topological Invariance under Line Graph Transformations
by Allen D. Parks
Symmetry 2012, 4(2), 329-335; https://doi.org/10.3390/sym4020329 - 08 Jun 2012
Viewed by 6321
Abstract
It is shown that the line graph transformation G L(G) of a graph G preserves an isomorphic copy of G as the nerve of a finite simplicial complex K which is naturally associated with the Krausz decomposition of L [...] Read more.
It is shown that the line graph transformation G L(G) of a graph G preserves an isomorphic copy of G as the nerve of a finite simplicial complex K which is naturally associated with the Krausz decomposition of L(G). As a consequence, the homology of K is isomorphic to that of G. This homology invariance algebraically confirms several well known graph theoretic properties of line graphs and formally establishes the Euler characteristic of G as a line graph transformation invariant. Full article
Show Figures

Figure 1

Previous Issue
Next Issue
Back to TopTop