A polyhedron is a 3D-shape that has flat faces, directly edges, and sharp vertices (corners). Words "polyhedron" is derived from a Greek word, where "poly" method "many" and hedron way "surface".Thus, when countless flat surfaces space joined with each other they form a polyhedron.

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1.Polyhedron Definition
2.Polyhedron Formula
3.Types that Polyhedron
4.Solved Examples
5.Practice Questions
6.FAQs ~ above Polyhedron

A polyhedron is a three-dimensional solid comprised of polygons. The has level faces, right edges, and also vertices. Because that example, a cube, prism, or pyramid are polyhedrons. Cones, spheres, and cylinders are non-polyhedrons since 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. For example, triangle prism, square prism, rectangle-shaped pyramid, square pyramid, and cube (platonic solid) space polyhedrons.Observe the following number which shows the different kinds the polyhedrons.

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Counting Faces, Vertices, and Edges

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

Face: The level surface the a polyhedron is termed together its face.Edge: The two faces meet in ~ a line dubbed the edge.Vertices: The point of intersection of 2 edges is a vertex.

Observe the following number which mirrors the face, vertex, and also edges that a shape.

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Polyhedron Formula


There is a relationship between the variety of faces, edges, and also vertices in a polyhedron. We have the right to represent this partnership as a mathematics formula well-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 = number of edgesBy utilizing the Euler"s Formula we can easily discover the lacking part of a polyhedron. Us can also verify if a polyhedron with the given number of parts exists or not. Because that example, a cube has actually 6 faces, 8 vertices (corner points) and 12 edges. Allow us examine whether a cube is a polyhedron or no 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 = number of edgesSubstituting the values in the formula: 6 + 8 - 12 = 2 ⇒ 2 = 2. Hence proved, cube is a polyhedron. 


Types of Polyhedron


Polyhedra space mainly separated into two species – continual polyhedron and also irregular polyhedron.Regular PolyhedronA regular polyhedron is additionally called a platonic heavy whose faces are consistent polygons and are congruent to each other. In a constant polyhedron, every the polyhedral angles space equal. There room five consistent polyhedrons. The adhering to is the list of five continuous polyhedrons.

Tetrahedron: A tetrahedron has actually 4 faces, 6 edges, and 4 vertices (corners); and also the form of each face is an it is intended triangle.Cube: A cube has 6 faces, 12 edges, and 8 vertices; and the shape of each challenge is a square.Regular Octahedron: A regular octahedron has actually 8 faces, 12 edges, and 6 vertices; and the form of each confront is an it is intended triangle.Regular Icosahedron: A regular icosahedron has 20 faces, 30 edges, and 12 vertices; and the shape of each challenge is an it is intended triangle.

Observe the following figure which shows the various varieties of consistent polyhedrons.

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Irregular PolyhedronA polyhedron v irregular polygonal deals with that room not congruent to every other, and in which the polyhedral angles are not equal is dubbed an irregular polyhedron.

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Convex PolyhedronA convex polyhedron is just like a convex polygon. If a line segment joining any type of two point out on the surface of a polyhedron completely lies within the polyhedron, it is called a convex polyhedron.

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Concave PolyhedronA concave polyhedron is quite comparable to a concave polygon. If a line segment joining any two point out on the surface of a polyhedron goes exterior the polyhedron, it is called a concave polyhedron.

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