Counting The Faces Edges And Vertices
Take a look at this gift box.
How many faces does it have?
Yes!
It has 6 rectangular faces.
When you put the faces together, it becomes a rectangular prism with 8 vertices and 12 edges!
Triangular Prism
Here’s a triangular prism shaped gift box:
How many faces does it have?
Correct! It has 5 faces.
But the faces are made of two different shapes.
2 are triangles and 3 are rectangles!
When you join the faces together, it becomes a triangular prism.
How many vertices does it have?
You got it!
How many edges does it have?
Yes! It has 9 edges!
Great work!
Take a look at this gift box:
It’s made up of 5 faces.
Are the shapes of the faces the same?
No, they’re not!
4 are triangles and 1 is a square.
When you join the faces together, it becomes a square based pyramid with 5 vertices and 8 edges!
Cylinder
Here’s a round gift box:
It has 2 circular faces that are considered the bases.
It has 1 curved surface.
A curved surface doesn’t count as a face. Faces are flat.
When you wrap the surface around the circles, it becomes a cylinder with 2 edges and 0 vertices.
Did you notice that a cylinder has no point?
That’s because a cylinder has no vertex.
Cone
Look at this party hat.
It’s made up of 1 surface and 1 circular face.
When you wrap the surface around the circle it becomes a cone with 1 vertex and 1 edge.
Faces Edges And Vertices Of A Sphere
A sphere has 1 curved surface, 0 flat faces, 0 edges and 0 vertices. A sphere is a 3D circle.
A sphere is ballshaped and is perfectly round, which means that it is not longer in a particular direction than any other.
A sphere contains no flat faces but it has one continuous curved surface. A sphere is a shape that contains no edges or vertices. This means that it feels smooth to touch all the way around.
It can help to pick up a spherical object and feel for edges and vertices. Whilst the net may be useful to help visualise the shape, we recommend using a ball or perfect sphere for this exercise as the net will be very difficult to make spherical with no clear edges or vertices.
What Are Vertices In Shapes
Vertices in shapes are the points where two or more line segments or edges meet . The singular of vertices is vertex. For example a cube has 8 vertices and a cone has one vertex.Vertices are sometimes called corners but when dealing with 2D and 3D shapes, the word vertices is preferred.
A cube has 8 vertices. 7 are visible here and one is hidden.
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Heres A List Of Shapes Along With The Number Of Vertices
3D Shape Vertices 

An edge in a shape can be defined as a point where two faces meet.

For example, a tetrahedron has 6 edges and a pentagon has 5 edges.

The line segments that form the skeleton of the 3D shapes are known as edges.

For a polygon, we can say that an edge is a line segment on the boundary joining one vertex to another.

A Tetrahedron has 6 edges.

For polyhedron shapes, a line segment where two faces meet is known as an edge.
How To Use Microsoft Edge To Solve Math Problems
Samir Makwana
Samir Makwana is a freelance technology writer who aims to help people make the most of their technology. For over 15 years, he has written about consumer technology while working with MakeUseOf, GuidingTech, The Inquisitr, GSMArena, BGR, and others. After writing thousands of news articles and hundreds of reviews, he now enjoys writing tutorials, howtos, guides, and explainers. Read more…
While there are several sites to learn math on, how about solving those problems inside your browser? Microsoft Edges new Math Solver makes it happen without breaking a sweat, and it can be a handy tool.
At the time of writing in June 2021, the Math Solver is still in the Preview stage and is available in Microsoft Edge 91. Clicking it opens a sidebar on the right side to clip and drop math problems or type them using the onscreen keyboard. From the looks of it, Math Solver might become a builtin feature like Collections.
Heres how you can use Microsoft Edge to solve math problems.
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Faces Edges And Vertices Of A Cuboid
A cuboid has 6 faces, 12 edges and 8 vertices. Each face of a cuboid is a rectangle. It is an elongated cube.
A cuboid is a 3D box shape and it has rectangular faces. A cuboid is also known as a rectangular prism.
A cuboid has 6 rectangular faces. The opposite faces on a cuboid are equal in size.
A cuboid has 12 edges. It has 4 horizontal edges around the top rectangular face and 4 horizontal edges around the bottom rectangular face. It also has 4 vertical edges connecting the vertices of the top rectangular face to the 4 vertices of the bottom rectangular face.
A cuboid has 8 vertices. It has 4 around the top rectangular face and 4 around the bottom rectangular face.
A cuboid has the same number of faces, edges and vertices as a cube. This is because a cube is a special type of cuboid that has all of its edges the same size.
The difference between a cube and a cuboid is that a cube has equal edge lengths, whereas a cuboid is longer in at least one direction.
When teaching 3D shape names, it is worth comparing a cube and cuboid alongside each other to identify the differences between the two.
The opposite faces on a cuboid are equal and can be coloured in the same colour on your net.
Faces Edges And Vertices Of A Square
A squarebased pyramid contains 5 faces, 8 edges and 5 vertices. The bottom face is a square and there are also 4 more triangular faces around the side of the shape. There are 4 vertices around the square base plus one more on the tip of the pyramid.
A squarebased pyramid contains 5 faces. The base is a square face and there are 4 triangular faces around the sides. These 4 triangular faces meet together at the tip of the pyramid.
The squarebased pyramid contains 8 edges. There are 4 horizontal edges around the square base and 4 more sloping edges between each triangular face.
The squarebased pyramid contains 5 vertices. There are 4 around the square base and one more at the tip of the pyramid.
The Egyptian pyramids are examples of reallife squarebased pyramids.
There are several types of pyramid, which are named by the face of the base.
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Example : Mbius Strip
A Möbius strip has 1 face and 0 vertices.
How many edges does it have?
An edge surrounds the face of a polyhedron.
2Count the number of faces / edges / vertices.
Look at this shape very carefully. Trace the edge, starting at 1 .
The Möbius strip has one edge.
Faces Edges And Vertices Of A Cone
A cone contains 1 flat circular face, 1 curved surface, 1 circular edge and 1 vertex. The vertex is formed from the curved surface and it is directly above the centre of the circular base.
A cone contains 1 flat circular face on its base. It also has a curved surface wrapping around this curved base. Technically it has 1 face in total but often the curved surface is included in the count to make 2 faces.
A cone contains 1 circular edge that wraps around the bottom circular face.
A cone contains 1 vertex which is on the very top of the shape directly above the centre of the circular base. It is formed from the curved surface.
It is possible that your child may mix a cone up with either a cylinder or a pyramid.
The difference between a pyramid and a cone is that a cone has a circular base and can roll on its side.
A cone and a cylinder both contain a circular base and you can hold the completed nets up and look directly at their base faces to see that they look identical from this orientation.
The cone converges to a point, whereas the cylinder does not.
You can compare how they roll to see the difference between them. A cone rolls in a circle because one end is wider than the other. A cylinder rolls in a straight line.
Traffic cones and icecream cones are common examples of the cone shape in reallife.
Now try our lesson on Classifying Angles as Acute, Obtuse, Right or Reflex where we learn how to describe angles.
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How To Calculate The Number Of Faces Edges And Vertices
In order to calculate the number of faces, edges and vertices of a 3D shape:
In order to count the number of faces, edges and vertices of a 3D shape:
*If there is an image of the 3D shape, note that some faces, edges and vertices may be hidden in the 2D representation.
Faces Edges And Vertices For Curved Surfaces
 Say: Take out your solid figures that have curved surfaces. Look at the sphere.
 Ask: Does a sphere have any edges or vertices? Why not?This is not a simple question and requires thinking critically about what an edge or vertex is. For example, many realworld objects that we call spheres, such as soccer balls, are in fact complex solid shapes with many edges and vertices. Consider using thinkpairshare, where students independently think through their reasoning, share it with a partner, and then you facilitate a discussion around how a sphere has no faces, so it cant have any edges, and because it has no edges, it cant have any vertices.
 Say: Look at the cone.
 Ask: Does a cone have any edges? Why not? Again, consider using thinkpairshare. Avoid telling students that they are right or wrong. Instead, lead them to see that a cone only has one face, and you need more than one face to form an edge.
 Ask: Does a cone have any vertices? Lead students to see that a cone has no edges , but the point where the surface of the cone ends is called the vertex of the cone.
 Say: Look at the cylinder.
 Ask: Does a cylinder have any edges or vertices? Why not? Although a cylinder has two faces, the faces dont meet, so there are no edges or vertices.
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Faces Edges And Vertices Of 3d Shapes
 Three dimensional shapes can be picked up and held because they have length, width and depth.
 Faces are the surfaces on the outside of a shape.
 Edges are the lines where two faces meet.
 Vertices are where two or more edges meet.
3 Dimensional shapes have length, width and depth.
The properties of a 3D shape are the number of faces, edges and vertices that it has.
 The above 3D shape is a cuboid, which is box shaped object.
 A cuboid has 6 rectangular faces, which are the outside surfaces of a 3D shape.
 A cuboid has 12 straight edges, which are the lines between the faces.
 A cuboid has 8 vertices, which are its corners where the edges meet.
 A cuboid has exactly the same number of faces, edges and vertices as a cube.
 A cuboid is different from a cube in that its edges are longer in at least one direction, whereas a cube has edges that are all equal in length.
Faces Edges And Vertices
Here we will learn about faces, edges and vertices including how to calculate the number of vertices, edges and faces of a 3D shape, and how to classify polyhedrons given the number of faces, edges and vertices.
There are also faces, edges and vertices worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if youre still stuck.
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Faces Edges And Vertices Of A Cube
A cube has 6 faces, 12 edges and 8 vertices. Each face of a cube is a square. All of its edges are the same length.
Each of the 6 faces of a cube is squareshaped because all of its edges are the same size. A cube is a 3D square.
There are 12 edges on a cube, which are all the same length. There are 4 horizontal edges around both of the top and bottom square faces. There are also 4 vertical edges connecting the top square face to the bottom square face.
There are 8 vertices on a cube. There are 4 vertices on the top square face and 4 vertices on the bottom square face.
Heres A List Of Shapes Along With The Number Of Edges
Shape 

An edge in a shape can be defined as a point where two faces meet.

For example, a tetrahedron has 4 edges and a pentagon has 5 edges.

The line segments that form the skeleton of the 3D shapes are known as edges.

For a polygon, we can say that an edge is a line segment on the boundary joining one vertex to another.

A Tetrahedron Has 6 Edges

For polyhedron shapes a line segment where two faces meet is known as an edge.
What are Faces?

A face of a figure can be defined as the individual flat surfaces of a solid object.

For example, a tetrahedron has 4 faces one of which is not visible.
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What Are Vertices Edges And Faces
3D shapes are made up of vertices, edges and faces.
Vertices are the pointy bits or the corners where edges meet.
Edges are the lines around a shape.
Faces are the sides that you touch when you hold a shape.
Take a look at this gift box:
It’s made up of 6squarefaces.
If you fold the faces and glue them together, it becomes a cube with 8vertices and 12edges!
Here’s a rectangular gift box:
It’s made up of 6 rectangular faces.
When you join the sides together, it becomes a rectangularprism with 8vertices and 12edges!
Here’s a triangular gift box:
It’s made up of 5 faces .
When you join the sides together, it makes a triangularprism with 6vertices and 9edges!
Here’s another triangular gift box:
It’s made up of 5 faces .
When you join the faces together, it becomes a square–basedpyramid with 5vertices and 8edges!
Here’s a round gift box:
It has 2circularfaces and 1surface.
The surface doesn’t count as a face. Faces are flat.
A cylinder has a curved surface with 2 edges and 0 vertices.
There are no sharp, pointy bits in a cylinder!
You can put lots of things inside these different shaped gift boxes!
What about cones?
Take a look at this party hat:
It’s made up of 1surface and 1circularface.
When you wrap the surface around the circle, it becomes a cone with 1vertex and 1edge.
What Are Faces Edges And Vertices
Faces, edges and vertices are features of a 3D shape.
 Faces are flat surfaces on the shape.
 Edges are straight lines that define the sides of the polygons that make up each face of the shape.
 Vertices are points where at least three edges meet.
To calculate the number of faces, edges and vertices of a 3D shape, we need to count the number of each using the 3D object.
Note, you need to be able to visualise the 3D object, you may not be given the shape to help you.
For example, a cube has 6 vertices, 12 edges and 6 faces.
Vertex  Edge  Face 
There are several 3D shapes that we need to know the number of vertices, edges and faces of.
Below is a diagram of common 3D shapes along with the number of vertices, edges and faces.
E.g. Polyhedrons flat faces, straight edges and sharp vertices.
Tetrahedron 
E.g. Nonpolyhedradont have flat faces, straight edges and sharp vertices.
Sphere 
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What Are Vertices In Math
Avertex is a mathematical word for a corner. Most geometrical shapes, whether two or three dimensional, possess vertices. For instance, a square has four vertices, which are its four corners. A vertex can also refer to a point in an angle or in a graphical representation of an equation.
TL DR
In math and geometry, a vertex the plural of vertex is vertices is a point where two straight lines or edges intersect.
How Do Vertices Faces And Edges Relate To Real Life
Any object in real life has vertices, faces and edges. For example, a crystal is an octahedron it has eight faces, twelve edges and six vertices. Knowing these properties for different threedimensional shapes lays the foundation for various industries such as architecture, interior design, engineering and more.
Recommended Reading: Three Basic Building Blocks Of Geometry
Vertices Faces And Edges Example Questions
1. Explain what a vertex is.
2.How many edges does a triangular prism have?
3.How many vertices does a cone have?
4. How many faces does a cuboid have? What are the 2D shapes of those faces?
5. For all the common prisms add the faces and vertices together and subtract the edges. What do you notice about the answers?
Wondering about how toexplain other key maths vocabulary to your children? Check out our Primary Maths Dictionary, or try these:
You can find plenty of geometry lesson plans and printable worksheets for primary school pupils on theThird Space Learning Maths Hub.
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