Irregular polyhedron


An irregular polyhedron is a three-dimensional geometric figure that does not meet the regularity condition. That is, their faces are not regular polygons (with sides and internal angles of equal measure) or identical to each other.

That is, an irregular polygon is the opposite case to a regular polygon.

Consider the case of a pyramid that has a square as its base and, at the same time, has four faces that are triangles.


Types of irregular polyhedron

The types of irregular polyhedron, depending on the number of faces it has, can be:

  • Tetrahedron: It has four faces. The trirectangle subcategory can be found which has three faces that are right triangles. These are those that have a right angle (which measures 90º). Thus, all these triangles join in a single vertex. On the other hand, we have the isofacial tetrahedron whose base is a right triangle and, in turn, the three faces are isosceles triangles (with two of their three sides of equal length) that are identical to each other.
  • Pentahedron: Five-sided polyhedron.
  • Hexahedron: It has six faces.
  • Heptahedron: Figure with seven faces.
  • Octahedron: It has eight faces.
  • Eneahedron: Its number of faces is nine.

Likewise, they can be distinguished:

  • Prisms: They have two identical and parallel faces (they do not intersect or when extended), called bases and are any two polygons. Likewise, the lateral faces are parallelograms (squares or rectangles, rhombuses or rhomboids). Its number of faces is equal to the number of sides that the parallel faces have plus two. That is, if the bases are pentagons, the total number of faces will be seven.
Pentagonal base prism
  • Pyramids: They are made up of a base that is any polygon and other faces (lateral) are triangles that meet at a common point (vertex). Pyramids can exist with many faces or sides.
Heptagonal pyramid

Another way to classify irregular polyhedra is according to their shape:

  • Convex: If when joining any pair of points of the polyhedron it is possible to do it by drawing a straight line that does not go outside the figure.
  • Concave: If at least two points of the polyhedron can be found that can be joined only by a straight line that does not always remain within the figure.
Concave polyhedron

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