Vertices, Faces and also Edges room the three properties the define any kind of three-dimensional solid. A vertex is the edge of the shape whereas a confront is a level surface and an edge is a right line in between two faces. 3d shapes faces, edges and also vertices, different from every other.

In our day-to-day life activities, we come across a variety of objects of different shapes and sizes. There room golf balls, doormats, ice-cream cones, coke cans and so on. These objects have different characteristic nature such as length, breadth, diameter, etc., which collection them apart from one another. Yet no issue how various their dimensions are, every one of them occupy an are and have three dimensions. So they are described as three-dimensional shapes or solids.

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There are figures that can be stood for on a plane (as a item of paper) and also have 2 dimensions, length, and also breadth. And they are referred to as two-dimensional or airplane figures. In this article, us will talk about the faces, edges and vertex definition in Maths because that the hard objects.


Table that contents:

What space Vertices?

The formal meaning for the vertex an interpretation in Maths is characterized as a point where two or much more edges meet. Vertices room the corner points.

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Cubes and also cuboids have 8 vertices.Cones have actually 1 vertex.Cylinders have no vertex.Spheres have actually no crest (the surface ar is a curve).

What room Faces?

Every individual flat surface that a hard is referred to as its face. Solids have much more than one face.

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Cubes and also cuboids have 6 faces.Cones have actually a flat face and a curved face.Cylinders have actually 2 flat faces and a bent face.A sphere has actually a bent face.

What room Edges?

The heat segment which acts together an interface in between two deals with is called an edge. Occasionally it is likewise described as the line segment joining 2 vertices.

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Cubes and also cuboids have actually 12 edges.Cones have 1 edge.Cylinders have 2 edges.Sphere has actually no edge.

Sides the Shapes

The word “side” is usually offered for polygon such together a square has 4 sides, a triangle has actually three sides, a pentagon has 5 sides.

Vertices, Faces and Edges of 3D shapes

Let us compare the vertices, faces and edges the solid shapes with the assist of a table.


Solid NameVertices Faces Edges
Cube86 (square faces)12
Cuboid86 (rectangular faces)12
Cone121
Cylinder032
Sphere010

Relation between Vertices, Faces and Edges (Euler’s Formula)

The relation between vertices, faces and also edges have the right to be easily determined with the help of Euler’s Formula. Having actually learned around the faces, edges, and vertices that solids, permit us note an amazing relationship between the three of them. It is to be retained in mind the the formula holds great for closed solids i m sorry have flat faces and also straight edges such as the cuboids. It can not be supplied for cylinders since they have actually curved edges.

Euler’s formula is given by

F + V – E = 2

Where F, V, and E space the variety of faces, vertices, and edges the the polyhedra respectively.

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Solved Examples

Q.1: A cube has actually 6 faces, 12 edges and also 8 vertices. Prove Euler’s formula for the cube.

Solution: Given, a cube has actually 6 faces, 12 edges and 8 vertices.

Therefore, follow to Euler’s formula,

 F + V – E = 2

Taking L.H.S.,

6 + 8 – 12

= 14 – 12

= 2 (R.H.S) 

Hence, proved.

Q.2: How numerous faces, edges and also vertices room there for a triangular prism?

Solution: A triangular prism is a polyhedron that has 5 faces, 6 vertices and 9 edges.

Practice Questions

What is the meaning of vertices?How numerous vertices are there because that a cone?Tell the number of edges for a sphere.A cylinder has 5 surfaces. True or false.

To learn much more about edges, faces, and also vertices meaning, recipe for different solid forms in Maths, download BYJU’S – The finding out App.

Frequently Asked questions – FAQs


What room vertices, faces and also edges?


Vertices room the corners of the three-dimensional shape, where the edges meet. Deals with are level surfaces and also edges space the lines wherein two deals with meet.

How many edges do a cone have?


A cone has one flat surface and also one curved surface. Therefore, it has actually only one edge where both the surface meet. It has a bent edge.

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How plenty of vertices a cube has?


A cube has 8 vertices.