Block Designs: Flywheel

reflection creates 4*2

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.


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