Patterns, parquetage, tessellation

Gio, Mar 14, 2015

For using in projekt Pontes (18.-21.3.2015)

Table of Contents

  1. Regular patterns
    1. Regular pattern
    2. Polygons and size of their interior angles
    3. Three Platon's parquetage
  2. Half-regular pattern
    1. 3-3-3-3-6
    2. 3-6-3-6
    3. 4-6-12
    4. 12-3-12
    5. 3-3-4-3-4
  3. Dual pattern
    1. The dual pattern to 4-4-4-4 and 3-3-3-3-3-3 system
    2. The Cairo Pentagon
  4. Escher's division of the plane and other tessellation
    1. Escher's tessellation using trasformation of a square
    2. Escher's tesselation
    3. Transformation of an equilateral triangle
    4. Transformation of a square
    5. Transformation of a hexagon

1.

Regular patterns

Which regular shapes will completely fill the whole plane?

  • 1. Regular pattern
  • 2. Polygons and size of their interior angles
  • 3. Three Platon's parquetage

1.1.

Regular pattern

– Gio

1.2.

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1.3.

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2.

Half-regular pattern

  • 1. 3-3-3-3-6
  • 2. 3-6-3-6
  • 3. 4-6-12
  • 4. 12-3-12
  • 5. 3-3-4-3-4

2.1.

3-3-3-3-6

– Gio

2.2.

–

2.3.

–

2.4.

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2.5.

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3.

Dual pattern

  • 1. The dual pattern to 4-4-4-4 and 3-3-3-3-3-3 system
  • 2. The Cairo Pentagon

3.1.

The dual pattern to 4-4-4-4 and 3-3-3-3-3-3 system

– Gio

3.2.

–

4.

Escher's division of the plane and other tessellation

  • 1. Escher's tessellation using trasformation of a square
  • 2. Escher's tesselation
  • 3. Transformation of an equilateral triangle
  • 4. Transformation of a square
  • 5. Transformation of a hexagon

4.1.

Escher's tessellation using trasformation of a square

– Gio

4.2.

–

4.3.

–

4.4.

–

4.5.

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Information