Analysis of Red Star
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
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,
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
Description of symmetries in a block:This
quilt is not made with blocks. Note that stitching follows the rhombic pieces
within the star. In the space outside the star, there are stitched flowers.
Unlike in the Nevada Star Quilt, these stitched "embellishments"
technically DO break the 8-fold dihedral symmetry.
Red Star Border Patterns
To see entire quilt, scroll up to the top.
TRVG, or 2*i
Analysis of quilt border (made from stitching in light mauve
In this pattern, the center line is a glide
mirror but not a reflection mirror. There are vertical mirrors and 2-fold
cyclic rotation centers mid-way between the vertical mirrors. The length of
the glide vector is the distance between vertical mirrors, and the length
of the translation vector is twice the glide vector.
TR, or 22i
Analysis of quilt border (made from stitching in dark mauve
In this pattern there are no mirrors or glide
mirrors. There are cyclic 2-fold rotation centers located at each "edge"
of a piece of rope and in the middle of each piece of rope. The translation
vector has length twice the distance between the centers.