Algorithm for generating quasiperiodic packings of icosahedral three-shell clusters

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dc.creatorCotfas, Nicolae
dc.date2005-04-14
dc.date.accessioned2026-07-07T04:32:01Z
dc.date.available2026-07-07T04:32:01Z
dc.descriptionThe strip projection method is the most important way to generate quasiperiodic patterns with predefined local structure. We have obtained a very efficient algorithm for this method which allows one to use it in superspaces of very high dimension. A version of this algorithm for two-dimensional clusters and an application to decagonal two-shell clusters (strip projection in a 10-dimensional superspace) has been presented in math-ph/0504036. The program in FORTRAN 90 used in this case is very fast (700-800 points are obtained in 3 minutes). We present an application of our algorithm to three-dimensional clusters. The physical three-dimensional space is embedded into a 31-dimensional superspace and the strip projection method is used in order to generate a quasiperiodic packing of interpenetrating translated copies of a three-shell icosahedral cluster formed by the 12 vertices of a regular icosahedron (the first shell), the 20 vertices of a regular dodecahedron (the second shell) and the 30 vertices of an icosidodecahedron (the third shell). On a personal computer Pentium 4 with Fortran PowerStation version 4.0 (Microsoft Developer Studio) we obtain 400-500 points in 10 minutes. More details, bibliography and samples can be found on the website: http://fpcm5.fizica.unibuc.ro/~ncotfas/
dc.descriptionComputer program in FORTRAN 90 and MATHEMATICA included
dc.identifierhttps://arxiv.org/abs/math-ph/0504044
dc.identifierhttp://arxiv.org/abs/math-ph/0504044
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/58038
dc.subjectMathematical Physics
dc.subjectMaterials Science
dc.subject52C23
dc.titleAlgorithm for generating quasiperiodic packings of icosahedral three-shell clusters
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