# A Model of Islamic Rectilinear
Interlaced Lattices

## INTERLACE

The interlace is a nonessential feature for the RIGE geometry, and in the eastern countries (from Persia
onwards) does not appear. However it is common in the Arabic countries and was in the Spanish Al-Andalus
and afterwards, in Christian commisioned* Mudejar* art (XIII- XVI cent.).
The universal way to achieve this interlace consists in passing the frame alternatively up and down the frames
which it crosses. This system always has a solution, it is always possible to interlace frames in an alternative up-
down basis.

Indeed, if we consider the polygons limited by the frames, we see that their sides are always segments of
frames between two crosses, or, if the frame bends, the fragment between crosses will give more sides, as
shown in the schema. Let us consider as positive the polygon whose sides begin in an up position and
finish down when going in the clockwise direction of gyration, and negative the opposite, as can be seen
in the schema above.

Since only two frames intersect at a time (R10), their crossing create four angles, two contiguous polygons
sharing only one segment of frame, and four polygons sharing a node. Now, it is easy to see that, if we select a
positive polygon, those contiguous to it will be negative, and the other one, opposed by the angle, positive. That
gives give us a rule to intersecting: we choose one polygon as positive and all the others will take their respective
direction; the frames will be then interwoven accordingly.

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Modelling a Rige

05-June-95