Geometric Figures and Polygons


Geometrical figures and polygons are studied in depth in mathematics, but also in art you need to have a basic knowledge of geometry to describe a work of art, plan its construction or make technical drawings.

Geometric figures: What they are and characteristics

A geometric figure is a non-empty set whose elements are points. These figures understood as geometric places are areas closed by lines or surfaces in a plane or in space. The geometric figures flat and solid, those with two or three dimensions respectively, are formed with the combination of other geometric figures more elementary and less dimension as the line or point.

For reasons of space and organization the rest of the article reports on the flat geometric figures. For more specific information on solid geometric figures, those with volume and therefore three-dimensional, go to the article ‘Geometric bodies’ (most common denomination).

What are the basic flat geometric figures

Flat geometric figures are those regions closed by non-aligned lines in a two-dimensional plane. These flat geometric figures are classified mainly into two types depending on whether their curved or straight lines:

Conics are the flat geometric figures delimited by a closed and flat curved line that result from the non-degenerate intersection between a cone and a plane that does not pass through its vertex. For example the circle and the ellipse. Polygons are the flat geometric figures delimited by the crossing of two or more straight lines, with three or more sides and the same number of angles.


Geometric Figures and Polygons

Types of polygons

The polygons are classified in turn into different types according to their properties based on the following criteria:

A) According to the measure of its sides and angles:

Regular polygon is one that can be inscribed in a circle because all its angles and sides are equal.
Irregular polygon is one whose vertices are not inscribed within a circle because their angles and sides are unequal.
Equilateral polygon is that with all its equal sides, but with angles of different measure.
Equiangular polygon is that with all its equal angles, but with sides of different length.

B) According to interior angles:

Convex polygon is that with interior angles of less than 180º and with all its diagonals (straight line joining two non-consecutive vertices) inside.
Concave polygon is that with at least one interior angle of more than 180º and with some external diagonal.

C) According to its axis of symmetry:

Symmetric polygon is that divisible with a line in equal halves. Asymmetric polygon is one that can not be divided with a line in equal halves.

Geometric Figures and Polygons

D) According to their number of sides or angles:
  • Triangle: Polygon with three sides or angles.
  • Quadrilateral: Polygon with four sides or angles.
  • Pentagon: Polygon with five sides or angles.
  • Hexagon: Polygon with six sides or angles.
  • Heptagon: Polygon with seven sides or angles.
  • Octagon: Polygon with eight sides or angles.
  • Enegon: Polygon with nine sides or angles.
  • Decagon: Polygon with ten sides or angles.
  • Hendecagon: Polygon with eleven sides or angles.
  • Dodecagon: Polygon with twelve sides or angles.
  • Tridecagon: Polygon with thirteen sides or angles.
  • Tetradecagon: Polygon with fourteen sides or angles.
  • Pentadecagon: Polygon with fifteen sides or angles.
  • Hexadecimal: Polygon with sixteen sides or angles.
  • Heptadecagon: Polygon with seventeen sides or angles.
  • Octadecagon: Polygon with eighteen sides or angles.
  • Enneadecagon: Polygon with nineteen sides or angles.
  • Icosagon: Polygon with twenty sides or angles.


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