# Red Pinwheel

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# Analysis of Red Pinwheel

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#### 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 pink

8) quilt block is shaded yellow

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#### Symmetries present:
reflection, glide reflection, translation

#### Description of symmetries: There
are horizontal reflection mirrors through the middle of the red strips and
no vertical mirrors. There are glide mirrors located through the centers of
the red strips both vertically and horizontally. The shortest translation
vector horizontally is the distance between the centers of the stars. The
shortest translation vector vertically is twice the distance between the centers
of the stars. The shortest glide vectors are the distance between the glide
mirrors both vertically and horizontally.

#### Description of fundamental region:
The fundamental region is the same as a block
with the addition of half of the red strip on all sides.

#### Description of symmetries in block:
Looking at an individual star within a block, we have cyclic 10-fold symmetry.

#### Relationship between block and fundamental region:
Again, the fundamental region is the same as a block
with the addition of half of the red strip on all sides.

#### Description of symmetries in quilting:
The quilter 'traced' the pattern of the quilt with no embellishments.
Thus, the quilting symmetry is in harmony with the quilt symmetry.