Special Issue "Polyhedra"

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

Deadline for manuscript submissions: closed (31 August 2012)

Special Issue Editor

Guest Editor
Prof. Dr. Egon Schulte
Northeastern University, Department of Mathematics, Boston, MA 02115, USA
Website: http://www.math.neu.edu/people/profile/egon-schulte
E-Mail: schulte@neu.edu
Interests: discrete and combinatorial geometry; combinatorics; group theory; graph theory

Special Issue Information

Dear Colleagues,

The study of polyhedra and symmetry has a long and fascinating history tracing back to the early days of geometry. With the passage of time, various notions of polyhedra have attracted attention and have brought to light new exciting classes of regular or other symmetric polyhedra including well-known figures such as the Platonic solids, Kepler-Poinsot star polyhedra, and Petrie-Coxeter sponge polyhedra, as well as the more recently discovered new regular or chiral skeletal polyhedra. This flexibility of the concept proves an important point --- polyhedra and symmetry have shown an enormous potential for revival! One explanation for this is the appearance of symmetric polyhedra in many contexts that a priori seem to have little apparent relation to symmetry, such as the occurrence of many figures in nature as crystals. In addition, their internal beauty appeals to the artistic senses and sparks the desire for a rigorous mathematical analysis and understanding of the figures themselves, as well as of their relationships with other areas of science.

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

Prof. Dr. Egon Schulte
Guest Editor

Keywords

  • regular polyhedron
  • symmetry group
  • classification by symmetry
  • polyhedron on a surface
  • abstract polyhedron
  • crystals
  • polyhedra in nature
  • polyhedral models
  • polyhedral design

Published Papers (10 papers)

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Displaying article 1-10
p. 54-80
by ,  and
Symmetry 2013, 5(1), 54-80; doi:10.3390/sym5010054
Received: 25 November 2012; Accepted: 5 December 2012 / Published: 9 January 2013
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(This article belongs to the Special Issue Polyhedra)
p. 47-53
by ,  and
Symmetry 2013, 5(1), 47-53; doi:10.3390/sym5010047
Received: 18 October 2012; in revised form: 18 December 2012 / Accepted: 31 December 2012 / Published: 7 January 2013
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(This article belongs to the Special Issue Polyhedra)
p. 1-46
by  and
Symmetry 2013, 5(1), 1-46; doi:10.3390/sym5010001
Received: 7 August 2012; in revised form: 6 December 2012 / Accepted: 7 December 2012 / Published: 28 December 2012
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(This article belongs to the Special Issue Polyhedra)
p. 644-666
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Symmetry 2012, 4(4), 644-666; doi:10.3390/sym4040644
Received: 24 August 2012; in revised form: 28 October 2012 / Accepted: 6 November 2012 / Published: 15 November 2012
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(This article belongs to the Special Issue Polyhedra)
p. 581-602
by ,  and
Symmetry 2012, 4(4), 581-602; doi:10.3390/sym4040581
Received: 2 September 2012; in revised form: 8 October 2012 / Accepted: 14 October 2012 / Published: 22 October 2012
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(This article belongs to the Special Issue Polyhedra)
p. 545-565
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Symmetry 2012, 4(3), 545-565; doi:10.3390/sym4030545
Received: 29 June 2012; in revised form: 13 August 2012 / Accepted: 19 August 2012 / Published: 30 August 2012
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(This article belongs to the Special Issue Polyhedra)
p. 336-343
by
Symmetry 2012, 4(3), 336-343; doi:10.3390/sym4030336
Received: 16 May 2012; in revised form: 20 June 2012 / Accepted: 25 June 2012 / Published: 3 July 2012
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(This article belongs to the Special Issue Polyhedra)
p. 265-275
by
Symmetry 2012, 4(2), 265-275; doi:10.3390/sym4020265
Received: 29 January 2012; in revised form: 26 March 2012 / Accepted: 5 April 2012 / Published: 16 April 2012
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(This article belongs to the Special Issue Polyhedra)
p. 208-218
by
Symmetry 2012, 4(1), 208-218; doi:10.3390/sym4010208
Received: 17 January 2012; in revised form: 21 February 2012 / Accepted: 23 February 2012 / Published: 27 February 2012
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(This article belongs to the Special Issue Polyhedra)
p. 1-14
by  and
Symmetry 2012, 4(1), 1-14; doi:10.3390/sym4010001
Received: 28 November 2011; in revised form: 15 December 2011 / Accepted: 19 December 2011 / Published: 28 December 2011
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Last update: 5 March 2014

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