Symmetry and Celtic Knots Exploration

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Objective: Symmetry in non-geometric shapes is quite interesting. Celtic art is quite symmetrical in nature.

Rozette groups

Recall that for a finite shape, we may classify it by its symmetry group. We first check if the figure has reflectional symmetry or not.

  1. If it does have reflectional symmetry, then it is denoted as a ‘D’ group.
  2. If it does not have any reflectional symmetry, then it is denoted as a ‘C’ group.
  3. Finally, we check what the largest degree of rotational symmetry is for our figure. This number is the added to the ‘D’ or ‘C’ we assigned before.

With Celtic art one should be careful! The under- and over-crossings have a tendency to destroy reflectivity. Hence most Celtic designs will be classified as a cylyc group Cn where n denotes the degree of rotational symmetry.

Design influenced by illustration in the Lindisfarne Gospels

On the right we see a knot that has 3-fold rotational symmetry and hence would be classsified as a C3.