Red Star




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 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. 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.

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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 strips)

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 strip)

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.

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