Pis Syabit 2

Photo courtesy of the Yuchengco Museum; piece from the Floy Quintos Collection


In the design of this pis yabit, one can find 5 squares with the same motif located at the center and the 4 corners; and 4 rectangles at every side.

The symmetries of the motif in each square consist of a vertical reflection, a horizontal reflection, two reflections with axes along the diagonals and a 90o rotation about the center. The symmetry group is D4.

The finite design of each rectangle has as symmetries a vertical reflection and a horizontal reflection, and a 180o rotation about the center. The symmetry group is D2.

Four layers of strip patterns frame the square found at the center.

-The first layer (starting from the innermost) has only translational symmetry. The symmetry group is 11.

-The third layer has vertical and horizontal reflections with axes that intersect at centers of 180o rotations. The symmetry group is mm.

-The second as well as the fourth layers have vertical reflections that alternate with 180o rotations, and glide reflection symmetry. The symmetry group is mg. These layers have the same symmetries as the strip patterns appearing at the borders of the pis yabit.

Zigzag strip patterns also with symmetry group mg surround the rectangles and the four squares at the corners.