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Regular Polygon

A regular polygon is a plane shape with equal sides and equal angles, which means that all sides and all angles of a regular polygon are in harmony.

Common examples of regular polygons are:

  1. Equilateral triangle
  2. Square
  3. Regular pentagon
  4. Regular hexagon
  5. Regular octagon


An equilateral triangle is a triangle with three equal angles and three equal sides.

The sum of angles of a triangle is equal to 180°. Since there are three angles in a triangle, each angle in an equilateral triangle is equal to 180°/2 = 60°

We know that the length and breadth of a square are equal.

l = b

Where, l = length and b = breadth

The perimeter (P) of a square is equal sum of the four sides of the square.

P = l + b + l + b

Since l = b,

P = l + l + l + l
    = 4l

'4l' implies that the four sides of the square are equal.

A square has four angles and each angle is equal to 90°.

The angles in a polygon can be obtained via the formular of the sum of the angles of an n-sided polygon, where n is equal to the number of sides of the polygon. The formular is (n-2)180°.

A pentagon is a 5-sided polygon, which means that n = 5. A hexagon is a 6-sided polygon where n= 6. And an octagon is a n 8-sided polygon where n = 8.

Apart from the equilateral triangle, the other four regular polygons are crucial to the study of the geometric structure of the harmonious universe. The regular hexagon, for instance, denotes the six square facets of the cube representing a balanced and stable world.

Bagua or Pakua is structurally an octagon. It is broken or Yin or two (even number) if it is an irregular octagon, and unbroken or Yang or one (odd number) if it is a regular octagon.

Therefore,

Broken (2) = Irregular Polygon

Unbroken (1) = Regular Polygon

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