Finite Symmetrical Patterns

A finite symmetrical pattern is a repeated pattern that does not admit any translational symmetry.

A finite pattern that has n-fold rotational symmetry or a 360o/n rotational symmetry but has no reflection symmetries has symmetry group the cyclic group of order n denoted by Cn.

Examples:

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A finite symmetrical pattern with the same symmetries as a regular n-gon, that is, has an n-fold rotational symmetry, and n reflection symmetries; has symmetry group the dihedral group of order 2n, denoted by Dn.

Example:

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