Final Exam Sample Problems
Here are some (not necessarily all) things you need to know how to do for the ﬁnal
exam.
ˆ
Write a symmetry in cycle notation; draw the diagram for a symmetry given in cycle
notation.
ˆ
Multiply symmetries. You should know how to multiply symmetries using diagrams
and how to multiply symmetries given in cycle notation without using a diagram.
Note that I can easily come up with problems that ask you to multiply symmetries
and for which a constructing a diagram would take too long to be done on an exam.
ˆ
Be familiar with the identity symmetry. Why is it called the identity symmetry?
ˆ
Given a symmetry
σ
, ﬁnd the inverse of
σ
. In particular, you need to understand
what it means for a symmetry to be the inverse of another symmetry [There is an
equation the two symmetries satisfy].
ˆ
How many symmetries does a given regular polygon have?
ˆ
You should be able to list all symmetries of a given regular polygon, both in cycle
notation and using diagram. Also be able to list all symmetries of a given polygon
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 Spring '08
 Staff
 Regular polygon, symmetries

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