Around the World
Analysis of Around the World
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
reflection, glide reflection, rotation, translation
Description of symmetries: There
are vertical, horizontal, and diagonal reflection mirrors at 45 degree angles
as shown.These mirrors are also glide mirrors : 4-fold dihedral rotation centers
are located at the intersection of four mirror lines. 2- fold dihedral rotation
centers are located at the intersection of two diagonal mirror lines. The
shortest translation generators are twice the distance between the diagonal
mirrors. The shortest glide vectors are twice the distance between the horizontal
and vertical mirrors.
Description of fundamental region:
An isosceles right triangle.
Description of symmetries in block: Interestingly,
here a block is two fundamental regions put together. As a block, it has a
reflection mirror through the center of the sector.
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 quilt embellishing
with only a border. Thus, the quilting symmetry is in harmony with the quilt
symmetry. For analysis of the border, see below.
Around the World Border Pattern
To see entire quilt, scroll up to the top.
TRVHG, or *22i
Analysis of hand-quilted border
There are vertical mirrors and the center line
is a horizontal mirror (and therefore a glide mirror.) The translation vector
of the strip pattern is equal to the distance from the center of one 'football'
to the center of the next 'football'. This vector is also the glide vector.There
are 2-fold dihedral centers at the intersection of the mirrors.