Block Designs: Plainsailing
translation creates 2*22
KEY:
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
generators
5) yellow points represent cyclic centers
6) light blue points represent dihedral centers
7) fundamental region is shaded purple
8) quilt block is identified above design
Symmetries present: reflection,
glide reflection, rotation, translation
Description of how design was made: We
made this pattern by translating the original block.
Description of symmetries in design: There
are diagonal (i.e at 45 degree angles to the horizontal) reflection mirrors.
These mirrors are also glide mirrors. Mid-way in between these mirrors are
glide mirrors that are NOT reflection mirrors. 2-fold cyclic rotation centers
are located at the intersection of 2 glide mirror lines; 2-fold dihedral rotation
centers are located at the intersection of 2 mirror lines. Translation generators
are the height and width of a block, as shown. The length of the shortest
glide vectors are half the diagonal of a block.
Description of fundamental region:
a rectangle that has mirrors as on three sides
and a glide mirror on the fourth side. Note that the 2-fold cyclic center
is located at the midpoint of one side while the 2-fold dihedral centers are
located at the vertices of the side opposite.
Description of symmetries in block:The
block displays 2-fold dihedral rotation at its center, which is present in
the larger design.
Relationship between block and fundamental region:A
fundamental region had one-fourth the area of a block.