How to Identify a Polyhedron

Let’s learn about polyhedrons and talk about faces, vertexes and edges. The problem is given to us want us to identify the number of faces, edges and vertexes on the three dimensional figures given below. Before we get on to identifying the faces, edges and vertexes, let’s actually understand what they are.

I am just going to draw a quick line and talk about what is a polyhedron? Polyhedron is a three dimensional figure so the key thing to remember is polyhedron is a three dimensional object that has flat surfaces. It has to have a flat surface. Each of these flat surfaces is called a face.

Now when two faces off a polyhedron meet, when two different faces meet, they form an edge. And when three or more edges meet, the point at which three or more edges meet is called a vertex. And the plural of vertex are vertexes, so knowing these let’s try and approach the figure.

So first one we can see is a cube, we need to first find number of faces. So we are looking for number of flat surfaces so as I can see this is a flat surface well this is one. The top is a flat surface that is two, this side is a flat surface that is three, those are three I can see from this side but there is one here which is four, there is one below which is five and there is one which is right up on top here which is six.

So as I can see it is a cube with six faces. Let’s count the number of edges, so this is an edge I am going to use a blue pen for the edge. This is an edge, this is an edge, this is an edge, because this face and this face are meeting, this is an edge so you can see four of edges right here. Then I have one here, one here, one here ands one here. Again this face and these faces meet so this is an edge so that is eight. Then I can see nine, 10, 11 and 12. So there are 12 edges.

Key to remember is an edge is the place where two faces meet. So at face six and face four meet this is the edge. How many vertexes are there? How many vertexes? Vertex is where three edges meet so this is edge one, two and three – they are meeting here. Let’s color that green so this is one, this is two then there is one here which is three. There is one here which is four, similarly I got four at the bottom, 1, 2, 3 and four and each one of these has three edges meeting as you can see. So they are eight vertexes so that is the first part.

Now let’s try the same thing with this polyhedron, first is this a polyhedron? Well it got four flat surfaces so it must be. Let’s count the number of surfaces or faces there is 1, 2, there is the behind one which is three and there is the bottom one which is four. So this one has four faces again I am going to change to color blue, how many edges? I got 1, 2, 3, 4, 5 and six there is only six edges, and how many vertexes? Well this place has one meeting for three, two, three and four so there are four vertexes.

Four faces, six edges and there are four vertexes, key thing to remember when we are looking at three dimensional objects, polyhedrons are three dimensional and have flat surfaces. Each flat surface is called a face, when two faces meet they form an edge and where three plus edges meet, three or more three edges meet that is called the vertex. And we can simply count those to get to the answers you are looking for.