From the Floy Quintos Collection

This elaborate waistband is adorned with geometric designs on both sides.

One side of the waistband consists of a repeating planar pattern.

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The symmetry group of this pattern is pmg.

There are 180o rotational symmetries with centers at the midpoint of a longer side (adorned with square designs) of every parallelogram. The vertical axes of reflection symmetries pass through a parallelogram’s shorter side.

Moreover portions of the band show squares with different motifs. Each pattern in a given square has symmetry group D4 .

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There is a 90o rotational symmetry about the center of the square and reflections with axes along the vertical, horizontal and diagonals passing through the center.

There are also three types of frieze patterns occupying a part of the waist band.

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This frieze has symmetry group mm. There are vertical reflections, a horizontal reflection and 180o rotational symmetries.

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The symmetry group of this frieze is 11. The pattern translational symmetries.

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The symmetry group is 12. There are 180o rotational symmetries. There are no reflectional symmetries.