Block Designs: Flywheel
reflection creates 4*2
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 pink
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. There are also diagonal glide mirrors. 4-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 half the translation generators (and sums of these create the shortest
horizontal and vertical glide vectors.)
Description of fundamental region:
an isosceles right triangle with mirror on its
hypotenuse. Note that the 4-fold cyclic center is located at right angle while
the 2-fold dihedral centers are located at the 45 degree angles (and are equivalent
by rotation.)
Description of symmetries in block:The
block displays only 4-fold cyclic rotation at its center, which is present
in the larger design.
Relationship between block and fundamental region:Four
fundamental regions make a block.