Hyperbolic Icosahedral Tilings by Buckyballs

• Authors: R. Lück , D. Frettlöh
• Languages of publication: EN

Abstracts

EN

Hyperbolic icosahedral tilings by Buckyballs with 4 or 8 Buckyballs sharing a vertex are considered as an example of tilings by Archimedean polyhedra. Representation requires Poincaré balls; colour symmetry may be derived by GAP. Colour symmetries preserving both rotation and reflection symmetry as well as only rotation symmetry are discussed.

Keywords

EN

02.20.-a; 61.48.-c; 61.50.Ah; 61.44.Br

Discipline

• 61.50.Ah: Theory of crystal structure, crystal symmetry; calculations and modeling
• 61.48.-c: Structure of fullerenes and related hollow and planar molecular structures(see also 81.05.ub Fullerenes and related materials in materials science)
• 61.44.Br: Quasicrystals
• 02.20.-a: Group theory(for algebraic methods in quantum mechanics, see 03.65.Fd; for symmetries in elementary particle physics, see 11.30.-j)

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 126
• Issue: 2
• Pages: 524-526

Dates

published

2014-08

Contributors

author

R. Lück

• Weilstetter Weg 16, 70567 Stuttgart, Germany

author

D. Frettlöh

• Bielefeld University, Technical Faculty, PB 100131, 33501 Bielefeld, Germany

References

• [1] M. Baake, J. Phys. A, Math. Gen. 30, 2687 (1997), doi: 10.1088/0305-4470/30/8/015
• [2] R. Lück, Philos. Mag. 88, 2049 (2008) and references therein, doi: 10.1080/14786430802056077
• [3] D. Frettlöh, Z. Kristallogr. 223, 773 (2008), doi: 10.1524/zkri.2008.1044
• [4] R. Lück, D. Frettlöh, Z. Kristallogr. 223, 782 (2008), doi: 10.1524/zkri.2008.1059
• [5] M.L.A.N. de las Peñas, R.P. Felix, G.R. Laigo, Z. Kristallogr. 221, 665 (2006), doi: 10.1524/zkri.2006.221.10.665
• [6] M.L.A.N. de las Peñas, R.P. Felix, G.R. Laigo, Z. Kristallogr. 225, 313 (2010), doi: 10.1524/zkri.2010.1220
• [7] M.L.A.N. de las Peñas, R.P. Felix, B.R. Gozo Jr., G.R. Laigo, Philos. Mag. 91, 2700 (2011), doi: 10.1080/14786435.2010.524901
• [8] GAP System for Computational Discrete Algebra, GAP - Groups, Algorithms and Programming http://www.gap-system.org
• [9] J. Humphreys, Reflection Groups and Coxeter Groups, series Cambridge Studies in Advanced Mathematics, No. 29, Cambridge University Press, Cambridge 1990; in Cambridge Books Online, Cambridge 2012, doi: 10.1017/CBO9780511623646

Identifiers

DOI

10.12693/APhysPolA.126.524