Wallpaper Objectives

1
Wallpaper Objectives

• Be able to classify a wallpaper pattern using
  centers of rotation and lines of reflection and
  glide reflection
• Be able to construct wallpaper patterns given a
  classification
• Be able to analyze cultural tilings using the
  classification

2
Locating centers and lines

• Tips for finding centers of rotation
• You should have a center of rotation at any point
  where lines of reflection meet.
• Look halfway between pairs of lines or pairs of
  rotation centers.

3
Locating centers and lines

• Tips for finding lines
• Check lines connecting rotation centers and lines
  between lines
• Look in all n directions around an n-gon

4
Classification

• Wallpaper patterns are classified using a four
  character string (just like frieze patterns).
• Rather than memorizing the rules for each
  character, we use the flow chart on page 163 and
  the table on page 162.

5
Examples
6
Double-checking your work

• Once you have identified a classification, you
  can check it at http//www.xahlee.org/Wallpaper_di
  r/c5_17WallpaperGroups.html

7
Generating a wallpaper pattern

• The image on the right shows how to generate a
  cmm pattern (the motif is placed in the shaded
  area the double lines stand for reflection).

8
Generating a wallpaper pattern

• Repeat the process with this generator for p4g.

9
Exam on Friday

• Covers
• dimensions of fractals using replacement rules
  and measurement
• building fractals using area
• analysis of artwork using fractals
• regular and semiregular tilings
• creating irregular tilings
• frieze patterns