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Amy Szczepanski's dihedral quilt...

Title: The Symmetries of the Square form a Nonabelian Group with Eight Elements (Migrations)
Artist and Designer: Amy F. Szczepanski
Materials: Cotton Fabric, cotton thread, and wool-polyester blend batting
Technique: Machine piecing and quilting

Artist’Äôs Description: The basic motif uses the Flying Geese pattern in a nine-patch block that has neither rotation nor reflection symmetry. The quilt consists of 64 of these blocks (32 of the original block and 32 of its mirror image) arranged in an 8-by-8 grid. The placement of the blocks was determined by writing down the 8-by-8 grid of the group table of the dihedral group (D_4 or D_8, depending on your preferred notation) and applying the group element in each space to the quilt block. The quilting pattern shows the quotient of the group by its center; this quotient is isomorphic to Z_2 x Z_2. The quilting pattern is sewn in two colors of thread (maroon and light green) and with two designs (loops and zig-zags). The four possible combinations of color and design are identified with the four elements ofZ_2 x Z_2, and the quilting pattern of each block represents the coset it belongs to in the quotient.