# Block Designs: Flywheel

# translation creates 442

#### KEY:

1) red segments represent reflection mirrors

2) light green segments represent glide mirrors that are not reflection mirrors

3) black 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 in either pattern. 2-fold cyclic rotation
centers are located at the midpoints of the sides of a block. Two kinds of
4-fold cyclic rotation centers are evident--one type is in the center of the
block and one type is where 4 blocks meet (at vertices of the block.) Translation
generators are the width and height of a block.

#### Description of fundamental region:
a square that has different 4-fold centers at
opposite vertices and equivalent 2-fold centers at opposite vertices.

#### Description of symmetries in block:The
block displays 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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