title: Merohedral twins revisited: quinary twins and beyond.
abstract: A twin is defined as being an external operation between two identical crystals that share a fraction of the atomic structure with no discontinuity from one crystal to the other. This includes merohedral twins, twins by reticular merohedry as well as coherent twins by contact where only the habit plane is shared by the two adjacent crystals (epitaxy). Interesting and original cases appear when the invariant substructure is built with positions belonging to the same {\bb Z}-module as, for example, the quinary twin structure first drawn by Albrecht Dürer [(1525). The Painter's Manual: a Manual of Measurement of Lines, Areas and Solids by Means of Compass and Ruler. Facsimile Edition (1977), translated with commentary by W. L. Strauss. New York: Abaris Books]. This paper will show that the Dürer twins, once defined in five-dimensional space, are simple merohedral twins, in the sense of Georges Friedel, leaving the five-dimensional lattice invariant. This analysis will be generalized to some other higher-order {\bb Z}-modules.
authors.affiliation: Laboratoire de Métallurgie de l'UMR 8247, IRCP Chimie-ParisTech, 11 rue Pierre et Marie Curie, F-75005 Paris, France.
authors.forename: Marianne
authors.initials: M
authors.lastname: Quiquandon
authors.affiliation: Laboratoire de Métallurgie de l'UMR 8247, IRCP Chimie-ParisTech, 11 rue Pierre et Marie Curie, F-75005 Paris, France.
authors.forename: Denis
authors.initials: D
authors.lastname: Gratias
authors.affiliation: Laboratoire de Métallurgie de l'UMR 8247, IRCP Chimie-ParisTech, 11 rue Pierre et Marie Curie, F-75005 Paris, France.
authors.forename: Abdullah
authors.initials: A
authors.lastname: Sirindil
authors.affiliation: Laboratoire de Métallurgie de l'UMR 8247, IRCP Chimie-ParisTech, 11 rue Pierre et Marie Curie, F-75005 Paris, France.
authors.forename: Richard
authors.initials: R
authors.lastname: Portier
keywords: Dürer structure; merohedral twins; polygonal tilings; quinary twins