## Homework!

Q1

Q2

Q3

Q4

Q5

Q6

Q7

Q8

Q9

Q10

Q11

Q12

Q13

### 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!

**Q15**Consider 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.

to outline

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