## The Four Basic Symmetries

POSSIBILITIES FOR THE COMPOSITION of a design are limitless, and may rely upon choices. But possibilities for the repetition of that design, whether symmetrical or asymmetrical, are limited by the laws of pattern formation and are subject to the constraints of symmetry.

IN ALL PATTERNS there are four basic symmetry operations that may be performed upon a fundamental region, design or motif. Mathematicians call these rigid motions because they suggest movements without distortion of size or shape around a point, along or across a line, or to cover a plane.

HERE, THE LETTER F (and the blank space around it) is taken as our fundamental region to demonstrate the four basic symmetry operations or rigid motions:

 translation rigid motion with repetition along a line reflection rigid motion with repetition across a line (axis) glide reflection rigid motion with reflected repetition along a line rotation rigid motion with repetition around a point

IN RUG-WEAVING, the repetition of a design to form a pattern is accomplished by counting and repeating sequences of knots. The basic symmetries in carpets are thus effected knot by knot.

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