{"title":"A milestone for the solution to the lattice sphere covering problem in dimension n = 6.","authors":"Frank Vallentin","doi":"10.1107/S2053273324011513","DOIUrl":null,"url":null,"abstract":"<p><p>The complete classification of (primitive, generic) parallelohedra in a given dimension is a challenging computational task. Nearly 50 years have passed since the classification for the last dimension, n = 5, was completed. One application of such a classification is in solving the lattice sphere covering problem for the corresponding dimension. The paper by Dutour Sikirić & van Woerden [Acta Cryst. (2025), A81, https://doi.org/10.1107/S2053273324010143] marks a milestone in the classification effort for dimension n = 6. It provides a complete classification of all primitive iso-edge domains; here primitive parallelohedra are identified based on their facet vectors.</p>","PeriodicalId":106,"journal":{"name":"Acta Crystallographica Section A: Foundations and Advances","volume":" ","pages":"5-8"},"PeriodicalIF":1.9000,"publicationDate":"2025-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Crystallographica Section A: Foundations and Advances","FirstCategoryId":"1","ListUrlMain":"https://doi.org/10.1107/S2053273324011513","RegionNum":4,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
The complete classification of (primitive, generic) parallelohedra in a given dimension is a challenging computational task. Nearly 50 years have passed since the classification for the last dimension, n = 5, was completed. One application of such a classification is in solving the lattice sphere covering problem for the corresponding dimension. The paper by Dutour Sikirić & van Woerden [Acta Cryst. (2025), A81, https://doi.org/10.1107/S2053273324010143] marks a milestone in the classification effort for dimension n = 6. It provides a complete classification of all primitive iso-edge domains; here primitive parallelohedra are identified based on their facet vectors.
期刊介绍：
Acta Crystallographica Section A: Foundations and Advances publishes articles reporting advances in the theory and practice of all areas of crystallography in the broadest sense. As well as traditional crystallography, this includes nanocrystals, metacrystals, amorphous materials, quasicrystals, synchrotron and XFEL studies, coherent scattering, diffraction imaging, time-resolved studies and the structure of strain and defects in materials.
The journal has two parts, a rapid-publication Advances section and the traditional Foundations section. Articles for the Advances section are of particularly high value and impact. They receive expedited treatment and may be highlighted by an accompanying scientific commentary article and a press release. Further details are given in the November 2013 Editorial.
The central themes of the journal are, on the one hand, experimental and theoretical studies of the properties and arrangements of atoms, ions and molecules in condensed matter, periodic, quasiperiodic or amorphous, ideal or real, and, on the other, the theoretical and experimental aspects of the various methods to determine these properties and arrangements.
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