Symmetry Definitions and Perception of Symmetry

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Symmetry Definitions and Perception of Symmetry
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Symmetry

• Definitions
• The concise Oxford Dictionary says
• " 1.(Beauty resulting from) right proportion
  between the parts of the body or any whole,
  balance, harmony, keeping. 2. Such structure as
  allows of an objects being divided by a point or
  a line or plane or radiating lines or planes into
  two or more parts exactly similar in size and
  shape and in position relative to the dividing
  point, ect. repetition of exactly similar parts
  facing each other or a centre,...."

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Type of symmetry - Rotation

• A figure has rotational symmetry when it can be
  rotated less than 360 around a central point, or
  point of rotation and still match the original
  figure
• Example

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Type of symmetry - Translation

• Move it without rotating or reflecting it
• Every translation has a direction and a distance
• Before translation

After translation
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Type of symmetry - Reflection

• Reflection symmetry is sometimes called "mirror"
  or "flip" symmetry.
• It's easy to see why A butterfly (see
  below) may have reflection
  symmetry
• because one side is a mirror image of
  the other.
•                                                
•                                 
                                                
• Notice that a vertical line down the center of
  the butterfly's body serves as what is called
  the "line of symmetry."

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Type of symmetry - Reflection

• The letter A has reflection symmetry similar to
  the butterfly.

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Type of symmetry - Glide Reflection

• Involves more than one step
• Combination of a reflection and a translation
  along the direction of the mirror line

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Symmetry groups- Platonic solids

• Definition

Platonic solids are perfectly regular solids with
the following conditions all sides are equal and
all angles are the same and all faces are
identical. In each corner of such a solid the
same number of surfaces collide. Only five
Platonic solids exist tetrahedron , hexahedron,
octahedron, dodecahedron and icosahedron
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Symmetry groups- Platonic solids

• The tetrahedron is bounded by four equilateral
  triangles. It has the smallest volume for its
  surface and represents the property of dryness.
  It corresponds to fire.

• The hexahedron is bounded by six squares. The
  hexadedron, standing firmly on its base,
  corresponds to the stable earth.

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Symmetry groups- Platonic solids

• The octahedron is bounded by eight equilateral
  triangles. It rotates freely when held by two
  opposite vertices and corresponds to air.

• The dodecahedron is bounded by twelve equilateral
  pentagons. It corresponds to the universe because
  the zodiac has twelve signs corresponding to the
  twelve faces of the dodecahedron.

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Symmetry groups- Platonic solids

• The icosahedron is bounded by twenty equilateral
  triangles. It has the largest volume for its
  surface area and represents the property of
  wetness. The icosahedron corresponds to water.

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Perception of Symmetry- Some psychological
observations

• The human face is approximately, symmetrical the
  difference are usually unnoticed .
• What happen when we mirror our face?

Original picture
Duplicate the right side
Duplicate the left side