Moroccan Geometry: S4: 8-fold with scissors, tessellated

8-fold with Scissors (Mtemen bil Maqoussa) متمن بل مقوسرة

The basic construction consists of 5 circles arranged in an X pattern. This yields an 8-fold pattern centered on a "reverse seal of solomon" with 4 sets of scissors pointing inward, alternating with 4 arrows pointing outward.

Alternatively, the pattern can be shifted diagonally by half of a panel, in which case the construction is based on 4 circles arranged in a square, and each circle touching another circle radiating from its diagnonal. This yields a pattern with a seal of Solomon at its center, surrounded by 4 scissors pointing outward, alternating with 4 "mgelsa", or seats.

In either pattern, each circle is divided into eighths, with marks along the horizontal, vertical, and both diagonal axes. All construction lines pass through these marks.

To tessellate the pattern on a 12"x18" page, you will repeat the 5 crossed circles six times.

The original class pattern consists of 4 circles arranged adjacently in a square, with another circle adjacent to each diagonal. This may be seen in full twice in the tessellation, and this pattern overlaps itself along the side circles.

If 8 is the top mark on each circle, then 1 is the first mark in the clockwise direction, etc. Begin the construction lines on the diagonal axes by connecting points 6 to 4 and 8 to 2 moving from NW to SE, then on the SW to NE axis, points 6 to 8 and 4 to 2. Extend the lines beyond the frame ONLY if they connect a similar set of points on the adjacent circles. Otherwise, extend the line only to the edge of the 5-circle frame, as illustrated below, where the yellow lines extend outside the basic frame while the purple lines do not.

Now connect the points 7 to 5 and 1 to 3 on the vertical axis, and points 7 to 1 and 5 to 3 on the horizontal axis. These lines may be extended over the length and width of the entire page.

Note the points where each vertical or horizontal meets a diagonal. Connect the opposite points along the horizontal, vertical, and diagonal axes. Once again, the horizontal and vertical lines will extend the entire page, while some of the diagonals will not. Each circle will have 16 lines passing through it.

Beginning with one of the central clusters of 4 circles, highlight the pattern in pencil, first with the seal of Solomon, then working outward from there.

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