About Symmetry

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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