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C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60.
TLDR
The icosahedral symmetry group H3 of order 120 and its dihedral subgroup H2 of order 10 are used for exact geometric construction of polytopes that are known to exist in nature and there is an uncountable number of different twisted fullerenes, all with precise icosahed symmetry. Expand
Breaking of Icosahedral Symmetry: C 60 to C 70
TLDR
This symmetry breaking process can be readily applied, and could account for and describe other larger cage cluster fullerene molecules, as well as more complex higher structures such as nanotubes. Expand
Faces of Platonic solids in all dimensions.
  • M. Szajewska
  • Mathematics, Medicine
  • Acta crystallographica. Section A, Foundations…
  • 6 April 2012
TLDR
This paper considers Platonic solids/polytopes in the real Euclidean space R(n) of dimension 3 ≤ n < ∞ and recursively decorating the appropriate Coxeter-Dynkin diagram provides the essential information about faces of a specific dimension. Expand
Reduction of orbits of finite Coxeter groups of non-crystallographic type
A reduction of orbits of finite reflection groups to their reflection subgroups is produced by means of projection matrices, which transform points of the orbit of any group into points of the orbitsExpand
Decomposition matrices for the special case of data on the triangular lattice of SU(3)
Abstract A method for the decomposition of data functions sampled on a finite fragment of triangular lattice is described for the cases of lattices of any density corresponding to the simple LieExpand
Four types of special functions of G 2 and their discretization
Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G 2, are compared and described. Two of the four families (called here C- andExpand
Icosahedral symmetry breaking: C(60) to C(84), C(108) and to related nanotubes.
TLDR
This paper completes the series of three independent articles describing the breaking of icosahedral symmetry to subgroups generated by reflections in three-dimensional Euclidean space as a mechanism of generating higher fullerenes from C60. Expand
Icosahedral symmetry breaking: C60to C84, C108and to related nanotubes
This paper completes the series of three independent articles [Bodner et al. (2013). Acta Cryst. A69, 583–591, (2014), PLOS ONE, 10.1371/journal. pone.0084079] describing the breaking of icosahedralExpand
Polytope contractions within icosahedral symmetry
Icosahedral symmetry is ubiquitous in nature, and understanding possible deformations of structures exhibiting it can be critical in determining fundamental properties. In this work we present aExpand
Faces of root polytopes in all dimensions.
  • M. Szajewska
  • Mathematics, Medicine
  • Acta crystallographica. Section A, Foundations…
  • 1 July 2016
In this paper the root polytopes of all finite reflection groups W with a connected Coxeter-Dynkin diagram in {\bb R}^n are identified, their faces of dimensions 0 ≤ d ≤ n - 1 are counted, and theExpand
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