Concave polyhedron


The concave polyhedron is one where to join at least two of its points it is impossible to draw a line segment that is inside the figure.

Another way to understand it is that this type of polyhedron has a dihedral angle (the one formed from the union of two faces) that is incoming. Consequently, a line can cut the surface of the figure at more than two points.

An additional way of explaining it is that when one of the faces of the concave polyhedron is prolonged, it cuts the figure.

We must remember that a polyhedron is a three-dimensional figure made up of faces that are polygons.

A concave polyhedron is the opposite of a convex one, which is one whose points can always be joined by a line that remains within the figure.

Elements of a concave polyhedron

The elements of a concave polyhedron are as follows:

  • Faces: They are the polygons that make up the sides of the polyhedron.
  • Edges: These are the segments where two faces of the figure meet.
  • Vertices: They are those points where several edges meet.
  • Dihedral angle: As we mentioned previously, it is the angle that is formed from the union of two faces. Their number is equal to the number of edges.
  • Polyhedron angle: It is one that is formed by the sides that coincide in the same vertex. Its number coincides with the number of vertices.

Examples of concave polyhedra

Some examples of concave polyhedra are as follows:

  • Prism with a pentagonal base: In this case, we have a prism whose bases are concave pentagons. Let us remember that a concave polygon is one that has at least one of its interior angles that measure more than 180º. In the case of the observed figure, the interior angle corresponding to the vertex E is greater than 180º.
  • Concave pyramid: It is that pyramid whose base is a concave polygon. For example, it may be a concave hexagon as we see in the figure below.
  • Other shapes: Concave polyhedra can have other shapes, such as the one we see at the bottom that resembles two steps on a ladder.

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