Tess takes a somewhat different approach to creating patterns than KaleidoMania. In Tess, you create a sketch using lines and/or polygons, and then apply combinations of symmetry operations or apply pattern types to the sketch.

Exploring the Software

• Begin by going to the Regular Polygon Tool. Read the help >> "Tool Tips" or leave the cursor over the tools to get directions on their use. Create a regular hexagon, and select an attractive color.
• Get the select tool. Note that this brings up five black sqaures that act as handles. Use the outside handles to rotate or change the size of the figure. Use the center handle to translate the figure without rotation.
• Use the Polygon Tool to create an irregular polygon of a different color. Each click creates a vertex. Double-click to finish. Use the select tool to identify and then modify the figure.
• Use the Hand Tool to move the whole field around.
• In the Symmetry Tool area, notice that the Symmetry Group default is C1. You can change this to any of a number of different symmetry groups. When you select a group this way, one or more of the Symmetry Operation Tools is automatically applied. You can also apply or un-apply specific symmetry operations.
• How do the symbols (on the image field) for the centers of rotations communicate their order (number of repetitions in a full rotation)?
• Note the additional options in the View menu.

Exploring the Mathematics

1. Why is the C1 symmetry group a good choice for the default?
2. What measures are available for the Rotation Tools? How does this affect the symmetry group options?