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.
You are watching: A flat surface of a polyhedron
|3.||Types that Polyhedron|
|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.
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.
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.
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.
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.
See more: 97 Grand Am Theft System Reset, How Do I Reset Security Code
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.
Related posts on Polyhedron
Check out the following articles related to the Polyhedron.