Rosette Symmetry Groups with Kali Exploration

Objective: Collect examples of symmetry groups. Gain exposure to the Kali software

Materials

• Printed copy of the Rosette Symmetry Groups with Kali Exploration.

Exploration

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/

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.

1. The top row of the Rosette Group menu shows patterns with the numbers 1 through 6. The full label of these groups is usually given as C1 through C6. Use Kali to draw examples for C2, C3, C4, C5 and C6. Copy these patterns onto your sheet you will be handing in.
2. The bottom row of the Rosette Group menu shows patterns with *1 through *6. The full label of these groups is usually given as D1 through D6. Use Kali to draw examples for D2, D3, D4, D5 and D6. Copy these patterns onto your sheet you will be handing in.
3. What rotational symmetry do the patterns have? Which ones have reflectional symmetry?
4. If someone told you they had a pattern that belonged to C24, what kind of rotational symmetry would it have? What kind of reflectional symmetry would it have?
5. If someone told you they had a pattern that belonged to D12, what kind of rotational symmetry would it have? What kind of reflectional symmetry would it have?

Handin: A sheet with answers to all questions.