Polarity (Opposite):
 

  The twelve signs are divided into six groups of two.
  Each group is called a polarity. Each sign has an
  opposite sign which expresses opposite characteristics.

Duality:
 
  The twelve signs are divided into two groups, 
  masculine or feminine.  Masculine are direct, out-
  going and energetic while Feminine are receptive,
  introspective and magnetic.

Triplicity (Element):
 
 The twelve signs are divided into four groups.
 Each three sign group is called a triplicity.
 They are grouped by their element - Earth, Air,
 Fire or Water.
     
 Aries, Leo and Sagittarius are Fire signs.
 Taurus, Virgo and Capricorn are Earth signs.
 Gemini, Libra and Aquarius are Air signs.
 Cancer, Scorpio and Pisces are Water signs.

Quadruplicity (Quality):

 The twelve signs are divided into three groups.
 Each of these groups are called a quadruplicity.
 Each of the quadruplicities indicate a quality.
 The three qualities are Cardinal, Fixed and
 Mutable. These qualities denote the sign's
 interaction with the outside world.

 Aries, Cancer, Libra and Capricorn are Cardinal
 signs. They are outgoing, creative and entreprising.

 Taurus, Leo, Scorpio and Aquarius are Fixed signs.
 They are resistant to change and perfectionists.

 Gemini, Virgo, Sagittarius and Pisces are Mutable
 signs. They are flexible and adaptable to change.