Sikiric, Mathieu DutourDelgado-Friedrichs, OlafDeza, Michel2015-12-100108-7673http://hdl.handle.net/1885/39066A 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 known 27 physical structures and the known special constructions by Frank-Kasper-Sullivan, Shoemaker-Shoemaker, Sadoc-Mosseri and Deza-Shtogrin.Keywords: Delaney symbols; exhaustive enumeration; Frank-Kasper structures201010.1107/S01087673100229322016-02-24