# Flowerbasket

# *x

# Analysis of Flowerbasket

#### 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 vertical mirror lines that pass through the center of each flowerbasket
and in between each pair of flowerbaskets. These mirrors are also glide mirrors.
There are also glide mirrors midway between each reflection mirror. The translation
generators we chose are as shown. The shortest glide vector is half the the
shortest vertical translation vector (the shortest vertical translation vector
can be made as a sum of the two translation generators shown.)

#### Description of fundamental region:
a rectangle that encloses half of a flower basket
(see above.) Its vertical edges

are reflection mirrors.

#### Description
of symmetries in pieces: This quilt is made from hexagonal
pieces rather than blocks. Ignoring color, the "field" of hexagons
produces a symmetry of *632. That is, a monochrome field of hexagons would
have 6-fold, 3-fold, and 2-fold dihedral rotation centers.