# Log Cabin

# 442

# Analysis of Log Cabin

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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:
rotation, translation (assuming that all dark 'stars' have
the same color/pattern)

#### Description of symmetries: There
are no reflection mirrors. There are 4-fold cyclic rotation centers located
at the centers of the 'star' shape in the blue figure and the red figure.
There are 2-fold cyclic rotation centers located at the intersection of the
small yellow squares.The shortest translation vectors horizontally and vertically
are the distance between the 4-fold cyclic centers. (Ignoring color, the shortest
diagonal translation vector would be the distance between the 4-fold cyclic
centers.)

#### Description of fundamental region:
The fundamental region is the same as the block
(i.e. one fourth of a blue star and one fourth of a red star together to form
a square.)

#### Description of symmetries in block:
Observing color, a block is assymetric. Ignoring color, the block would have
rotation by a cyclic 2-fold center.

#### Relationship between block and fundamental region:
They are the same.

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