## Homework!

### Cutting an orbifold

Now we just saw a few neat things. Take a pattern, you can get a surface unique to a motif. Now we show you how to get ALL POSSIBLE motifs for a given symmetry from the orbifold. Just cut the thing open, keeping track of mirror lines, fold corners and cone points, until you can lay it flat. Cut open any way you like. That will be a choice of motif. No matter how you do it. And every motif can be obtained in this way

Q14 Examine GSP sketches inf.inf and 5. These sketches (and many of the other sketches in the part IV of last weeks homework) allow you to slide the boundaries between motifs. That is, they let you change your choice of motif. How does this sliding look as moving a cut around on the corresponding orbifolds?

### SubSymmetries Revealed!

Q15Consider inf.inf and *inf.inf. Which is a subsymmetry of the other? Similarly consider *n and n. What are their orbifolds? Is there a way to get the orbifold of one from the other? Draw this

333 is a subsymmetry of 3*3 and *333. Can you get the orbifolds of the last two by doing something to the orbifold of 333? Draw this.

Repeat the exercise for 442, 4*2, and *442. Draw this.

Q16: A symmetry's orbifold can be obtained from a subsymmetry's orbifold by ........

Q17

### The Orbifold Store!

Aw, we'll save it for next time.

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