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Updated: Jun 10, 2026
Probing C84-embedded Si Substrate Using Scanning Probe Microscopy and Molecular Dynamics
Published on: September 28, 2016
Space fullerenes: a computer search for new Frank-Kasper structures
Mathieu Dutour Sikirić1, Olaf Delgado-Friedrichs, Michel Deza
1Rudjer Bosković Institute, Bijenicka 54, 10 000 Zagreb, Croatia. mdsikir@irb.hr
Abstract:
A Frank-Kasper structure is a 3-periodic tiling of the Euclidean space E3 by tetrahedra such that the vertex figure of any vertex belongs to four specified patterns with, respectively, 20, 24, 26 and 28 faces. Frank-Kasper structures occur in the crystallography of metallic alloys and clathrates. A new computer enumeration method has been devised for obtaining Frank-Kasper structures of up to 20 cells in a reduced fundamental domain. Here, the 84 obtained structures have been compared with the known 27 physical structures and the known special constructions by Frank-Kasper-Sullivan, Shoemaker-Shoemaker, Sadoc-Mosseri and Deza-Shtogrin.
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