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A. Borovik, Gel'fand Im, N. White (2003)
Reflection Groups and Coxeter Groups
L. Schlaefli
Réduction d'une intégrale multiple, qui comprend l'arc de cercle et l'aire du triangle sphérique comme cas particuliers.Journal de Mathématiques Pures et Appliquées
W. McKay, J. Patera (1981)
Tables of Dimensions, Indices, and Branching Rules for Representations of Simple Lie Algebras
R. Moody, J. Patera (1992)
Voronoi and Delaunay cells of root lattices: classification of their faces and facets by Coxeter-Dynkin diagramsJournal of Physics A, 25
L. Boya, Cristian Rivera (2012)
On Regular PolytopesReports on Mathematical Physics, 71
B. Champagne, M. Kjiri, J. Patera, R. Sharp (1995)
Description of reflection-generated polytopes using decorated Coxeter diagramsCanadian Journal of Physics, 73
(1993)
A Coxeter diagram description of faces of Voronoi cells and their duals
Vinay Deodhar (1982)
On the root system of a coxeter groupCommunications in Algebra, 10
Robert Moody, Jiri Patera (1995)
Voronoi Domains and Dual Cells in the Generalized Kaleidoscope with Applications to Root and Weight LatticesCanadian Journal of Mathematics, 47
J. Burckhardt (1953)
Réduction d’une intégrale multiple, qui comprend l’arc de cercle et l’aire du triangle sphérique comme cas particuliers
W. Fischer, Marburg (1990)
Sphere Packings, Lattices and GroupsZeitschrift Fur Kristallographie, 191
D. Mckenzie, C. Davis, D. Cockayne, D. Muller, A. Vassallo (1992)
The structure of the C70 moleculeNature, 355
D. Manolopoulos, P. Fowler (1995)
An Atlas of Fullerenes
M. Bodner, J. Patera, M. Szajewska (2013)
C70, C80, C90 and carbon nanotubes by breaking of the icosahedral symmetry of C60.Acta crystallographica. Section A, Foundations of crystallography, 69 Pt 6
T. Hales (1998)
Sphere packings, IDiscrete & Computational Geometry, 17
This paper considers Platonic solids/polytopes in the real Euclidean space of dimension 3 ≤n < ∞. The Platonic solids/polytopes are described together with their faces of dimensions 0 ≤d≤n− 1. Dual pairs of Platonic polytopes are considered in parallel. The underlying finite Coxeter groups are those of simple Lie algebras of types An, Bn, Cn, F4, also called the Weyl groups or, equivalently, crystallographic Coxeter groups, and of non‐crystallographic Coxeter groups H3, H4. The method consists of recursively decorating the appropriate Coxeter–Dynkin diagram. Each recursion step provides the essential information about faces of a specific dimension. If, at each recursion step, all of the faces are in the same Coxeter group orbit, i.e. are identical, the solid is called Platonic. The main result of the paper is found in Theorem 2.1 and Propositions 3.1 and 3.2.
Acta Crystallographica Section A Foundations of Crystallography – Wiley
Published: Jul 1, 2014
Keywords: ; ; ; ;
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