Symmetry groups of Friezes and Wallpaper patterns
- Kali is a program developed
by Nina
Amenta, Jeff
Weeks, and Mark
Phillips at the
former Geometry Center at the University
of Minnesota to help you draw patterns with any given symmetry group,
either one of the seven frieze symmetry groups, or one of the 17 wallpaper
symmetry groups. There are several ways to access Kali. The easiest way
if you have a Java-capable web-browser is just to
click here and then click
the link
labeled Run the
program. You should see a drawing palette to the right and several
buttons to the left for the different symmetry groups. The program begins
showing wallpaper groups, but you can use the pull-down menu under
"Wallpaper Groups" to choose "Frieze Groups". Versions of Kali for various
platforms are available for downloading at
the Kali
home page.
- Introduction to
Symmetries is
a nice web-based short course by Chaim Goodman-Strauss.
- Wallpaper
patterns is another web-based short course by Chaim Goodman-Strauss
that explains how
to use Kali to explore symmetries of wallpaper patterns and includes some
exercises and homework.
- An excerpt from the CRC Standard Mathematical Tables and
Formulas covering Geometry
Formulas and Facts is available on the web at
the Geometry Center at
the University of Minnesota. Of special interest is a discussion of
the 5 types of Symmetries
of the Plane, including links to formulas
in cartesian coordinates and other coordinates. There is also a list
and discussion (with pictures) of the 17
Wallpaper Groups.
- A different viewpoint is found in the collection of handouts for Geometry
and the Imagination in Minneapolis, a two-week summer workshop lead by
John Conway, Bill Thurston, and others. This contains for example a
discussion of symmetry
from a somewhat different viewpoint than we've taken; you may have to read
previous sections of the document to understand some of this. At the end
is a field
guide to the orbifolds discussing again the 17 symmetry groups, their
names, and a photostat of some manuscript pages of Conway's.
Mail comments and suggestions concerning this site to
saper@math.duke.edu
Last modified: 08/24/2011 16:52:17