We have already defined that a centered pattern at least one unique point that fits into the pattern differently than any other point.

Patterns that have only rotational symmetry will be described as a CYCLIC pattern. We will use the symbol C_N to describe a pattern that has only N-fold rotational symmetry.

Note that it is understood that N>1. In fact, C₁ is the designation for an asymmetrical design, since it would repeat itself exactly one time in a full rotation.

Every cyclic pattern has only one unique point, which is the center of rotation of the pattern or design.

Patterns that have both rotational and mirror symmetries will be described as DIHEDRAL patterns. We will use the symbol D_N to describe a pattern that has N-fold rotational symmetry with N apparent mirrors.

Again, it is understood that N>1. In fact, D₁ is the designation for a design that has only one mirror, and is described as having simple bilateral (two sided) symmetry. Such a design may or may not have rotational symmetry.

Unlike friezes or tessellations, which repeat predictably to infinity, centered patterns are predictable only as far out from the center as they are represented. That is, beyond the furthest design element already represented, you can not predict what element will be added next.