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Icosahedral Symmetry and Magnetism

MRS Proceedings, 1986
AbstractWe examine the implications of icosahedral symmetry on electronic structure and especially magnetic properties in alloys. From simple geometric and synmetry arguments to detailed electronic structure calculations it is clear that icosahedral symmetry carries important consequences for magnetism in a wide range of alloys. Enhanced local magnetic
M. E. McHenry, R. C. O–
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Icosahedral symmetry carbon cage molecules

Nature, 1986
Graphite, when vaporized by laser irradiation, produces a very stable cluster of 60 carbon atoms which, it has been suggested, takes the uniquely elegant form of one of the archimedian semiregular polyhedra—the truncated icosahedron1,2. In considering the possibility of other structures of especial stability, we are led by a sequence of fairly general ...
D. J. Klein, W. A. Seitz, T. G. Schmalz
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Icosahedral symmetry in clusters

Progress in Crystal Growth and Characterization of Materials, 1997
First principles calculations and simulations based on interatomic potentials together with experimental studies of abundance spectrum suggest icosahedral structures to be common for some magic clusters of diverse systems such as rare gases, metals, covalently bonded systems and water.
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Probing Local Icosahedral Symmetry

Europhysics Letters (EPL), 1987
It is shown that crystal field splitting of rare-earth or actinide ions at sites with icosahedral point symmetry is extremely simple, unique, and even predictable. It is expected to survive in any icosahedrally coordinated solid state, like in quasi-crystals or metallic glasses.
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Coronal holes and icosahedral symmetry

Solar Physics, 1988
A new type of coordinates suitable to describe mass outflow out of coronal holes assuming symmetry under the icosahedral group is introduced.
Wolfram Neutsch, Horst Fichtner
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Symmetries of Icosahedral Quasicrystals

1991
The icosahedral group A(5) as the point symmetry group of quasicrystals is by now well established for a variety of materials. Quasicrystals have been grown up to macroscopic scale and display polyhedral shapes with this symmetry, compare the review by Guyot, Kramer and de Boissieu 1990 [1].
P. Kramer, Z. Papadopolos, D. Zeidler
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Polytope contractions within icosahedral symmetry

Canadian Journal of Physics, 2014
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 a framework for generating and representing deformations of such structures while the icosahedral symmetry is preserved.
M. Bodner, J. Patera, M. Szajewska
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Symmetry of icosahedral quasicrystals

Structural Chemistry, 2015
The concept of infinitely fragmented fractal tiling is proposed for the description of the structure and symmetry of quasicrystals. Fractal tilings may serve as unique “parent” structures for the corresponding local isomorphism class. The generating symmetry elements and some special features of the resulting symmetry groups of the fractal tilings are ...
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Depictions of Icosahedral Symmetry

Journal of Geological Education, 1992
Pentagonal icosahedral symmetry has been discovered recently in quasicrystals of aluminum alloys and the pure carbon molecule, buckminsterfullerene. The stereographic projection of icosahedral symmetry is an interesting exercise that challenges students to look beyond the 32 normal crystal classes.
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Crystal-field splitting in icosahedral symmetry

Physical Review B, 1987
The crystal-field splitting of rare-earth ions in icosahedral symmetry is treated by group-theoretical and numerical methods. From the crystal-field Hamiltonian, which is governed by only one crystal-field parameter, the crystal-field splitting schemes of all rare-earth ions in their Hund's-rule ground state are derived.
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