# Block Designs: Signature

# translation creates 2222

#### KEY:

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

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#### 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. 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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