## What do all those symbols *mean *

**Q8:** Have you made any observations so far about
the notation?

In particular, does anything leap out about the symbol *****?

How about **o**

The notation on the rosette palette should be familiar from last week
and will form the basis for the additional notation.

For now we'll focus on the symmetries on the first three rows of the
wallpaper palette. . .

##### For each pattern...

1) In kali sketch a pattern for reference. Save it!

2) Change colors and mark each center of rotation-- make each look a
little different if possible.

Change colors and mark all lines of reflection. If you can make two
lines
of reflection look different, do it! Do the same for any glide lines.

So for example, here we have a four-fold center of rotation, a single
way to draw a mirror line, and a single two-fold center of dihedral
symmetry:

______________

3) Save your work now! You may have to experiment a while to do the next
part. You can always reload your saved sketch!

4) Now: How MANY of each kind of center of rotation are there?

In the example shown here, there is one KIND of dihedral center of order
2, and one KIND of cyclic center of order 4. Note that the name of the
symmetry
is **4*2**...

Also note that the lines of reflection, & the centers of rotation
lie on the boundaries between motifs.

**Q9:**Write down your motif and generators on the
sheet. As you get a few done, look closely! Can you figure out how the
notation
works? One clue-- the numbers before a *****mean something just a little
different than the numbers after.

When you've done a bunch
of these, you're surely ready for some real fun:
A cool connection!

to outline

**Chaim Goodman-Strauss**
Dept. Mathematics
Univ. Arkansas
Fayetteville, AR 72701
*strauss@comp.uark.edu*
* 501-575-6332*