Symmetry and Orbifolds

Objectives:

  1. To determine the orbifold for a particular symmetry
  2. To determine the topological surface from the symmetry group of a tiling

Materials Needed:

Comment:

An orbifold is a motif on layered paper that when unfolded creates a symmetrical tiling with the motif. A paper doll is an example of an orbifold. When you cut out the figure and unfold the paper you create a pattern of the figure.

Activity 1:

Given a pattern of a motif on Templates C ,D, and
  • Glide
  • Rotational
  • Reflection
  • Glide reflection

    Activity 2:

    Using Template     G combine basic "folding" techniques to create the orbifold for the shown tilings.

    Question:

    Using Symmetry and Orbifolds Worksheet indicate the surfaces that generate the chosen symmetries. Use templates H, I, K, and