Celtic Art Exploration 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. - If there is reflectional
symmetry, then the symmetry group is called a dihedral group,
abbreviated 'D'. - If there is no reflectional symmetry, then
the symmetry group is called a cyclic group, abbreviated 'C'. -
Finally, we check what the highest order of rotational symmetry
is for our figure. This number is appended to the ‘D’ or ‘C' to
form the symmetry group name. With Celtic art one should be
careful! The under- and over-crossings have a tendency to
destroy reflection symmetry. Hence most Celtic designs will be
classified as a cyclic group Cn where n denotes the degree of
rotational symmetry. Above we see a knot that has 3-fold (order
3) rotational symmetry and hence would be classsified as a C3.
Determine the Rosette Groups for these Celtic Knots: - Celtic
Knotwork: the Ultimate Tutorial A Look at the Construction and
Mathematics of Celtic Knot