# Butterfly

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# Analysis of Buttefly

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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 (ignoring colors
of butterflies)

#### Description of symmetries: There
are vertical reflection mirrors located through the center of the butterfly's
body and also through the center of the pink vertical strips.These mirrors
are also glide mirrors. The shortest translation vector horizontally is twice
the distance between vertical mirrors and the shortest vertically are the
distance between the centers of the blocks. The shortest glide vectors are
the same length and directions as the shortest translation vectors.

#### Description of fundamental region: A
rectangle with vertical sides mirrors and horizontal sides at lines through
the center of the pink horizontal strips between blocks.(i.e. half of a butterfly
block)

#### Description of symmetries in block: As
a block, there is vertical reflection through the center of the butterfly's
body.

#### Relationship between block and fundamental region:
A block is approximately 2 fundamental regions.

#### Description of symmetries in quilting:
The quilter 'traced' the pattern of the butterfly and 'filled
in' the rest of the quilt with horizontal and vertical quilted strips which
alternate directions in the blocks. Thus, the quilting symmetry is not in
harmony with the quilt symmetry.

There is also a quilted 'fern' border or strip pattern (not visible in the
photo). See below.

# Butterfly Border Pattern

### To see entire quilt, scroll up to the top.

# THG, or i*

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## Analysis of hand-quilted border

## The translation vector of the strip pattern
is equal to the distance from the left stem of the fern to the left stem of
the next fern.This is also the glide vector.The horizontal reflection mirror
(which also acts as a glide mirror) is perhaps approximate due to the slightly
askew right most leaf of the fern.