Analysis of Buttefly


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 (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.

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Butterfly Border Pattern

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THG, or i*


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.

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