We examine in this paper what may be termed Islamic Geometric Art, however it is also found in other religions, such as Jewish and Christian, Eastern (Syriac, Coptic) and Western (Mudejar Art, from Al-Andalus, Spain). Earlier forms can be seen in Roman and Byzantine Art, as well. But its main development is related to Islam, in Al-Andalus, Maghreb, Egypt, Turkey, Persia, Afghanistan, Pakistan and Islamic India. See references [Audsley,1968. Bourgoin, 1973. Bourgoin, 1977. Burckhardt, 1972 and 1976. Cabanelas, 1988. Critchlow, 1992. Grabar, 1984. Jawad al-Janab, 1982. Martínez, 1976. Nuere, 1989. Ögel,1987. Pavón Maldonado, 1981, 1990. Prieto y Vives, 1977. Sánchez, 1993-a. Sánchez, 1993-b. Speltz, 1959. Wilson, 1988.].

We will focus on a particular but representative branch of this geometric art: the Rectilinear Lace, which we will call RIGE ("Red Islámica Geométrica Entrelazada", islamic interlaced geometrical lattice). We shall try to find the formal parameters which define this branch, and therefore separate it from other modalities of decoration, existing or possible. Of course, we do not intend to exhaust this intricate matter, nor explain everything about it; we are only raising a number of questions and begin to answer them, showing perhaps ways to follow on with a further study. Our experience is that, the more one draws designs and thinks about them, the more beautiful possibilities and properties are brought to light, giving a strong basis and unity to that branch of the Islamic Decorative Arts (in Arabic, zákhrafa ) [Cabanelas, 1988. Prieto y Vives, 1977. Nuere, 1989.].

Hence we shall not deal with historical considerations and cultural heritages. Only a few metaphysical remarks will be made; it could not be otherwise, given the strong numerical and symbolic aroma which pervades this particular form of art.

First, we shall propose a set of axiomatic formal rules which model, in our opinion, those forms. Afterwards, we shall develop, comment, even contradict, those rules, showing the relation between geometry and art.

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