Friezes, continued

1
Friezes, continued

• Pick a motif that has no symmetry of its own.
• Create two frieze patterns (one spinning, one
  not) with that motif. Do not indicate what type
  of pattern you are using.
• Trade patterns with the person next to you and
  classify their patterns.

2
Wallpaper Patterns

• Motivation how many different ways are there to
  tile a plane?
• Strategy identify the use of the isometries.

3
Reflections

• Use red (or dashed) lines to indicate lines of
  reflection.

4
Glide Reflections

• Use blue (or dashed) lines to indicate lines of
  glide reflection.

5
Rotations

• Place an n-gon for a center of n-fold rotation.
  (Our book shades the n-gon if if it on a
  reflection line.)

6
Practice

• For each of the following patterns, find all
• reflection lines
• glide reflection lines, and
• n-fold rotation centers

7
More on Rotations

• Only 2-fold, 3-fold, 4-fold, and 6-fold rotations
  are possible.
• Why 5-fold rotation doesnt exist
• Find a pair, A and B, of 5-fold rotation centers
  which are as close together as possible.
• Rotate B about A and A about B to create another
  pair of 5-fold rotation centers that are even
  closer together.

8
Next Week

• Project Proposals due 3/12
• Next Exam 3/14