Block Designs: Chainlink
reflection creates 2*22
KEY:
1) red segments represent reflection mirrors
2) light green segments represent glide mirrors that are not reflection mirrors3)
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 reflecting the original block horizontally, then reflecting
2 blocks vertically, then 4 blocks horizontally, etc..
Description of symmetries in design: There
are vertical, 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 length of a
diagonal of the block, as shown. The shortest glide vectors are the width
and height 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 cyclic rotation at its center, which is present in the
larger design.
Relationship between block and fundamental region:Two
fundamental regions make a block.