Block Designs: Chainlink

translation creates 2222

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: rotation, translation

Description of how design was made: We made this pattern by translating the original block.

Description of symmetries in design: There are no mirrors or glide mirrors in the pattern. 2-fold cyclic rotation centers are located at each vertex of a block, at the midpoints of sides of blocks, and at the center of each block as shown. Translation generators are the width and height of a block.

Description of fundamental region: a rectangle that has 2-fold cyclic centers at each vertex and at the midpoints of a pair of opposite sides.

Description of symmetries in block:The block displays only 2-fold cyclic rotation at its center, which is also present in the larger design.

Relationship between block and fundamental region: Two fundamental regions make a block.


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