# Texas Star

# *8

# Analysis of Texas Star

#### 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,
rotation

#### Description of symmetries: There
are 8 mirrors and an 8-fold dihedral rotation center at the intersection of
the mirrors. Thus this pattern is a wheel pattern, not a wallpaper pattern.

#### Description of fundamental region:
an "inifintely extending" whose sides
are mirrors, and center of the sector is the rotation center of the pattern.
Note that above the sector looks like a triangle, but imagine it extending
outward forever.

#### Description of symmetries in a block:This
quilt is not made with blocks. This quilt appears
to be the same structure as the Nevada Star. However, outside the star pattern
in this quilt, the stitching appears to continue the pattern of the pieces
(rhombuses.) This stitching contrasts with Red Star, where the quilting breaks
the symmetries and Nevada Star, where the quilting may not break the symmetry
but does depart from the geometry of the pieces.