By Steurer Walter, Sofia Deloudi
ISBN-10: 364201898X
ISBN-13: 9783642018985
ISBN-10: 3642018998
ISBN-13: 9783642018992
From tilings to quasicrystal constructions and from surfaces to the n-dimensional technique, this publication provides a whole, self-contained in-depth description of the crystallography of quasicrystals. It goals not just at conveying the strategies and an actual photograph of the constructions of quasicrystals, butit additionally allows the reader to go into the sector of quasicrystal constitution research. Going past metal quasicrystals, it additionally describes the recent, dynamically growing to be box of photonic quasicrystals. The readership may be graduate scholars and researchers in crystallography, solid-state physics, fabrics technology, strong- nation chemistry and utilized mathematics.
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Freeman and Company, New York (1987) 10. P. Gummelt, Penrose tilings as coverings of congruent decagons. Geom. Dedic. 62, 1–17 (1996) 11. P. Gummelt, Decagon clusters in perfect and random decagonal structures. In: Quasicrystals. Ed. -R. Trebin, pp. 90–104, VCH Wiley (2003) 12. P. Gummelt, C. Bandt, A cluster approach to random Penrose tilings. Mater. Sci. Eng. A 294, 250–253 (2000) 46 1 Tilings and Coverings 13. T. Hahn, H. Klapper, Point groups and crystal classes. In: International Tables for Crystallography, vol.
Chem. Phys. 10, 147–167 (1942) 16. L. Henley, Sphere Packings and Local Environments in Penrose Tilings. Phys. Rev. B 34, 797–816 (1986) 17. L. Henley, Random tiling models. In: Quasicrystals. The state of the art. P. J. Steinhardt. World Scientific, Singapore, pp. 459–560 (1999) 18. L. Henley, V. Elser, M. Mihalkovic, Structure determinations for randomtiling quasicrystals. Z. Kristall. 215, 553–568 (2000) 19. K. Ingersent, in: Quasicrystals. The state of the art. P. J. ), World Scientific, Singapore, pp.
A polyhedron can also be characterized by its vertex configuration, which just gives the kind of polygons along a circuit around a vertex. A polyhedron {p, q} has the vertex configuration pq . 1 We will use the notion introduced by Lord, E. , Mackay, A. : New Geometries for New Materials. 1 Convex Uniform Polyhedra 51 Fig. 2. The five Platonic solids inscribed in cubic unit cells to show their orientational relationships to the 2- and 3-fold axes of the cube: tetrahedron, {3,3} 33 , octahedron, {3,4} 34 , hexahedron (cube), {4,3} 43 , icosahedron, {3,5} 35 , dodecahedron, {5,3} 53 The dual {q, p} of any of the Platonic solids {p, q} is a Platonic solid again.
Crystallography of Quasicrystals: Concepts, Methods and Structures by Steurer Walter, Sofia Deloudi
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