Repetition and Illusion of Infinity
Most patterns are derived from a grid of polygons such as equilateral triangles, squares, or hexagons. The mathematical term for these grids is "regular tessellation" (deriving from the Latin tesserae, i.e., pieces of mosaic), in which one regular polygon is repeated to tile the plane. (See activity.) No matter how complex or intricate a design becomes, it is still predicated on a regular grid. Most geometric ornamentation is based on the premise that every pattern can be repeated and infinitely extended into space. This means that a frame can appear to be arbitrary, simply providing a window onto a pattern that continues beyond the bounds of that frame.
Symmetry
Symmetry is created in Islamic geometric design through the repetition and mirroring of one or more basic design units—usually shapes such as circles and polygons. Although the design can be elaborated and made complex, the basic symmetrical repetition and mirroring of these shapes creates a sense of harmony.
Two-dimensionality
Most Islamic geometric design is two-dimensional. Not only is it generally applied to flat surfaces, but the patterns themselves rarely have shading or background-foreground distinction. In some instances, however, an artist will create interlocking or overlapping designs that create the illusion of depth and produce an aesthetically pleasing and visually playful composition.
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