A Model of Islamic Rectilinear Interlaced Lattices

Fig.6. "Alcazar". Design.

DISPLACEMENT PLANE COVERING

In periodic lattices, it is often found that parts of the form repeat themselves on the plane by translation (displacement) in two dimensions, until they cover the plane, or a part of it. This kind of repetition is suitable for actually covering big surfaces in a sort of treillis or canevas. See Fig.6-7, Alcazar, whose original covers the inner Patio of the Alcazar of Seville.

To carry out this translation, a new element must also be found and defined: the Translation Element (TE) of the form. This constitutes a usual type of decorative procedure, sometimes actually realized in physical form, such as the wood block that Indian tinters use to cover a silk cloth. The relative situation of the repeated TE must also be defined: when TE is rectangular, its repetitions can be situated in columns and rows; or in displaced rows, like bricks in a wall. Other shapes of TE would need a different disposition to cover the plane, like the hexagon, in a bee-panel pattern; see, again, [Coxeter,1973. Ghica, 1977. Rademacher & Toeplitz,1970.].

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05-June-95

A Model of Islamic Lattices.1.