Sikiric, Mathieu Dutour; Delgado-Friedrichs, Olaf; Deza, Michel
A Frank-Kasper structure is a 3-periodic tiling of the Euclidean space E3by 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...[Show more]
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