Red Pinwheel

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Analysis of Red Pinwheel

 

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

 

 

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.


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