POSSIBILITIES FOR THE COMPOSITIONof 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 PATTERNSthere 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.

[About Symmetry and Pattern]

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