Frieze Patterns.

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Presentation transcript:

Frieze Patterns

Definition: An infinite strip with a symmetric pattern There are only 7 frieze patterns if we use one color

Types of Friezes: 1. Translation symmetry only: 2. Glide reflection plus translation symmetry: 3. Reflection over a horizontal line plus translation:

More Types: 4. Reflection over a vertical line plus translation: 5. Rotation (a half-turn about a point on the midline of the strip) plus translation: 6. Reflection over a vertical line plus a reflection over a horizontal line plus translation: 7. Reflection over a vertical line plus glide reflection plus translation:

Examples

Creating a Frieze Step 1: Cut out a block letter Step 2: Reflect your letter over a vertical line (Now there are 2 pieces to your basic design: the original letter and its reflected image) Step 3: Take your design (2 elements) and reflect them over the horizontal line Step 4:Translate the image by a fixed distance. NOTE: We have created a basic element with all symmetries.