# Frieze Marking Exploration

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**Objective:**
Learn to recognize symmetries of frieze patterns.

### Materials

- Two copies of File: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:

- On the paper, mark all symmetries for each pattern:
- Mark the length of the translation.
- Mark any reflectional symmetry by drawing the mirror lines.
- If there is a glide reflection, mark the length of the translation and label that arrow with a G.
- Mark any centers of rotation with a diamond.

- Identify the frieze group for each pattern.
- What is going on with pattern #8?

**Handin:**
The paper of strip patterns, marked with symmetries and the frieze groups.