Block Designs: Chainlink

translation or rotation 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 (left image) or rotating the original block (right image.)

Description of symmetries in design: There are no mirrors or glide mirrors in either pattern. In the pattern made by translation, 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. In the pattern made by rotation, 2-fold cyclic centers are located at the vertices and in the center of each block. Translation generators are the length of a diagonal 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 (in both cases.)

Relationship between block and fundamental region: In the pattern made by translation, two fundamental regions make a block. In the pattern made by rotation, the block and the fundamental region have the same area.


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