Frieze Marking Exploration

From EscherMath

Materials

• Two copies of Image:Blocky.pdf, one printed on paper and one on a transparency.
• Scissors

Procedure

• Cut the transparency into eight strips as indicated.
• First test for vertical and horizontal reflection symmetry. You can fold up the paper and check if there is a match.
• For each strip pattern on the paper, use the corresponding transparency strip as an overlay to test for the remaining symmetries:
  • Test for glide-reflections: Can you make the frieze pattern match up if you reflect the trip and slide it horizontally?
  • Test for rotational symmetry: Does the frieze look the same if you turn it through 180 degrees?

Answer the following questions:

1. On the paper, mark all symmetries for each pattern:
   1. Mark the length of the translation.
   2. Mark any reflectional symmetry by drawing the mirror lines.
   3. If there is a glide reflection, mark the length of the translation and label that arrow with a G.
   4. Mark any centers of rotation with a diamond.
2. Identify the frieze group for each pattern.
3. What is going on with pattern #8?