Block Designs: Chainlink

rotation creates 442

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 rotating the original block.

Description of symmetries in design: There are no mirrors or glide mirrors in the pattern. 2-fold cyclic centers are located at in the center of each block. 4-fold cyclic centers are located at the vertices of each block. Translation generators are the length of a diagonal of a block.

Description of fundamental region: a square that has 4-fold cyclic centers at opposite vertices and 2-fold cyclice centers at opposite vertices.

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

Relationship between block and fundamental region: A block has twice the area of the fundamental region.


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