A polyhedron is a 3D-shape that has level faces, directly edges, and also sharp vertices (corners). The word "polyhedron" is obtained from a Greek word, where "poly" means "many" and also hedron means "surface".Thus, when many flat surfaces are joined with each other they type a polyhedron.

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1. | Polyhedron Definition |

2. | Polyhedron Formula |

3. | Types the Polyhedron |

4. | Solved Examples |

5. | Practice Questions |

6. | FAQs on Polyhedron |

A polyhedron is a three-dimensional solid made up of polygons. It has level faces, directly edges, and vertices. For example, a cube, prism, or pyramid space polyhedrons. Cones, spheres, and also cylinders are non-polyhedrons due to the fact that their sides are not polygons and also they have actually curved surfaces. The many of a polyhedron is also known as polyhedra. They are classified together prisms, pyramids, and also platonic solids. Because that example, triangle prism, square prism, rectangle-shaped pyramid, square pyramid, and cube (platonic solid) space polyhedrons.Observe the following figure which mirrors the different kinds that polyhedrons.

**Counting Faces, Vertices, and also Edges**

The size of a polyhedron room classified together faces, edges, and also vertices.

Face: The level surface that a polyhedron is termed as its face.Edge: The two faces meet in ~ a line referred to as the edge.Vertices: The point of intersection of two edges is a vertex.Observe the following number which reflects the face, vertex, and also edges of a shape.

## Polyhedron Formula

There is a relationship in between the variety of faces, edges, and also vertices in a polyhedron. We deserve to represent this partnership as a math formula known as the Euler"s Formula.Euler"s Formula ⇒ F + V - E = 2, where, F = variety of faces, V = number of vertices, and also E = variety of edgesBy making use of the Euler"s Formula we have the right to easily discover the lacking part of a polyhedron. Us can also verify if a polyhedron v the given number of parts exists or not. Because that example, a cube has actually 6 faces, 8 vertices (corner points) and also 12 edges. Let us examine whether a cube is a polyhedron or not by utilizing the Euler"s formula. F = 6, V = 8, E = 12 Euler"s Formula ⇒ F + V - E = 2 where, F = variety of faces; V = number of vertices; E = variety of edgesSubstituting the values in the formula: 6 + 8 - 12 = 2 ⇒ 2 = 2. For this reason proved, cube is a polyhedron.

## Types the Polyhedron

Polyhedra are mainly separated into two varieties – consistent polyhedron and irregular polyhedron.**Regular Polyhedron**A consistent polyhedron is also called a platonic solid whose deals with are regular polygons and are congruent to every other. In a consistent polyhedron, all the polyhedral angles space equal. There are five continual polyhedrons. The adhering to is the list of five consistent polyhedrons.

**Tetrahedron:**A tetrahedron has 4 faces, 6 edges, and also 4 vertices (corners); and also the shape of every face is an it is intended triangle.

**Cube:**A cube has 6 faces, 12 edges, and 8 vertices; and the form of each challenge is a square.

**Regular Octahedron:**A continual octahedron has 8 faces, 12 edges, and 6 vertices; and the shape of each face is an it is intended triangle.

**Regular Icosahedron**: A continuous icosahedron has 20 faces, 30 edges, and 12 vertices; and also the form of each confront is an it is provided triangle.

Observe the following figure which shows the various types of continual polyhedrons.

**Irregular Polyhedron**A polyhedron with irregular polygonal encounters that room not congruent to each other, and in i beg your pardon the polyhedral angles room not same is dubbed an rarely often, rarely polyhedron.

**Convex Polyhedron**A convex polyhedron is similar to a convex polygon. If a heat segment joining any type of two point out on the surface ar of a polyhedron entirely lies inside the polyhedron, the is referred to as a convex polyhedron.

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**Concave Polyhedron**A concave polyhedron is quite similar to a concave polygon. If a heat segment joining any two points on the surface of a polyhedron goes external the polyhedron, the is referred to as a concave polyhedron.

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