The due date for the symmetry project is coming up (on 4/19) and now that we are at the end of the symmetry unit, I want to make sure you have all the information that you need to complete the project.

- This introduction to symmetry is useful for anything you may have missed in class.
- Rosettes are covered in the above introduction to symmetry. These patterns can be divided into two groups:
- Rosettes that have only rotational symmetry, which are group C#, where the # indicates the order of rotation. For example, C99 has a rotation of order 99, C2 has a rotation of order 2 (180 degrees or halfway around a circle).
- Rosettes that have both rotational and reflectional symmetry, which are group D#. The # indicates the number of mirrors and the order of the rotation, which are equal in all of these patterns. For example, D99 has 99 mirrors and a rotation of order 99, D2 has two mirrors and a rotation of order 2 (180 degrees or halfway around a circle).

- Friezes are reviewed at EsherMath and you can also review our notation for the frieze patterns.
- Wallpaper patterns are covered at EscherMath, Wikipedia, and in the website with examples that I showed you in class
- Are you curious about why you can get 2, 3, 4, and 6-fold rotational symmetry, but not 5-fold rotational symmetry (order 5 rotations) in wallpaper patterns. This is a great article that explores that issue, and how to create patterns that appear to have 5-fold symmetry.

- Rosettes are covered in the above introduction to symmetry. These patterns can be divided into two groups:
- To create symmetry images, you can take pictures of patterns in the world, make your own drawings, or use computer tools to create patterns. Some useful tools:
- Kali: http://www.geom.uiuc.edu/java/Kali/welcome.html
- Artlandia SymmetryMill: http://www.artlandia.com/products/SymmetryMill/
- A simple rosette creator (with a fixed symmetry type): http://www.permadi.com/java/spaint/spaint.html
- Ambigrams are words that can be read in multiple ways and are in generally symmetric — you can find some useful tools here for creating them: http://www.scottkim.com/inversions/
- Another wallpaper pattern creator: http://jcrystal.com/steffenweber/JAVA/jwallpaper/J2DSPG.html
- Snowflake creator (only creates one symmetry type): http://snowflakes.barkleyus.com/ (although can’t you just cut a snowflake on your own?)

- You should post your pieces on flickr in the symmetry group for the course. If you do not have a flickr account, use the class flickr account to upload your images (user id: mathartdesign & password:lesley). See the description of the project for what you need to include with your images and how many images you need — the only constraints on your images is that they should be created by you!

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