Symmetric Figures Exploration

From EscherMath

Kali is a Java based program that lets you draw symmetrical patterns based on rosette, frieze and wallpaper groups. You select the symmetry group and a basic pattern; Kali produces the rest. This program can be found online at: http://www.geom.uiuc.edu/java/Kali/

1. Think of symbols, icons and logos with symmetry. Using one index card for each, draw four good pictures. Make your pictures big and dark, and try to be accurate.

Now run the computer program Kali. Kali contains a large drawing window, color selector buttons, a group-type selector (initially set to Wallpaper), and group selector buttons . For this exercise, change the group-type selector from Wallpaper to Rosette, then select one of the buttons below that. (You may have to press a group button more than once to make the change to that group take effect.)

Play around with the different Rosette symmetry groups. Click on a few and try drawing lines in the drawing window.

2. Use Kali to redraw one or two of your symbols from part 1.
3. Figure out which Kali symmetry groups correspond to each of your symbols from part 1, and label the symbols with the corresponding number (or starred number).
4. Come up with a well known symbol that has a different symmetry than the ones you’ve seen so far, and draw it on a fresh index card.