Analysis of Blue Pattern
1) red segments represent reflection mirrors
2) light green segments represent glide mirrors that are not reflection mirrors
3) dark blue segments represent translation generators
4) dark green segments represent shortest glide vectors that are not translation
5) yellow points represent cyclic centers
6) light blue points represent dihedral centers
7) fundamental region is shaded pink
8) quilt block is shaded yellow
reflection, glide reflection, rotation, translation
Description of symmetries: There
are vertical, horizontal, and diagonal reflection mirrors at 45 degree angles
as shown.These mirrors are also glide mirrors : 4 fold dihedral rotation centers
are located at the intersection of four mirror lines. Two fold dihedral rotation
centers are located at the intersection of two mirror lines (specifically
vertical and horizontal intersections with no diagonal mirrors through them.)
The shortest translation vectors horizontally and vertically are twice the
distance between the horizontal and vertical mirrors. ( Similarly, the shortest
diagonal vectors are twice the distance between the diagonal mirrors, but
all diagonal vectors can be made from the horizontal and vertical vectors.)
The shortest glide vectors are the same length and directions as the shortest
translation vectors with the addition of a diagonal glide vector.
Description of fundamental region: The
fundamental region is an isosceles right triangle with sides mirrors and vertices
of legs at the 4-fold dihedral centers and the right angle at the dihedral
Description of symmetries in block: As
an individual block, it has dihedral 4-fold symmetry.
Relationship between block and fundamental region:
A block is approximately 4 fundamental regions.
Description of symmetries in quilting:
The quilter 'traced' the pattern of the quilt with no embellishments.
Thus, the quilting symmetry is in harmony with the quilt symmetry.