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 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, 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.

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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.

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