Table of Faces

We’re now going to continue with the worksheet and do column C. column C is the regular kind of thing that’s done when studying platonic solids. We look at the number of edges and the number of vertices, and so on. But to help us in this, we can use Oilers formula for convex polyhedra, which is that the number of faces plus the number of vertices minus the number of edges always equals two. And I’ll put that on the worksheet in the last row. So we can check when we do h solid that this is true. This is the same as the table on your worksheet. So we’re going to have to fill out the table for each platonic solid. You’ll see at the bottom there, I’ve got f plus V minus V equals two. Again, I’m going to give you 30 seconds. This time it’s to fill out the table. The shape of each face is a nega lateral triangle, number of faces meeting at each vertex, three number of faces. For the number of vertices, we have four triangles. So that’s 12 vertices. But we have three faces meeting at each vertex. So that is for the number of edges. We have four triangles, so that’s 12 edges, but each edge is shared by two faces. So that six does f plus V minus equal to. We have four plus four is eight minus six equals two. Next solid is the cube. You have 30 seconds The shape of each face is a square. The number of faces meeting at each vertex is three. The number of faces is six. The number of vertices. six squares gives us 24 vertices that we have three faces meeting at each vertex. So that will be eight. The number of edges. Well six squares gives 24 edges, but two faces share each edge So that’s 12 does f plus V minus equal to six plus eight is 14 minus 12 is two and the next solid is the octahedron 30 seconds. The shape of each face is a nickel lateral triangle. number of faces meeting at each vertex is four number of phases, eight number of vertices We have eight triangles, that’s 24 vertices for faces meet at each vertex. So that will be six number of edges. I triangles gives us 24 edges. each edge is shared by two faces. So the answer is 12. Does f plus V minus equal to eight plus six is 14 minus 12 is two. The next solid is the dodecahedron 30 seconds The shape of each face is a regular pentagon. The number of faces meeting at each vertex three number of faces 12. The number of vertices 12. Pentagon’s give us 60 vertices. And the three phases of meeting at each vertex, give us 20. And the number of edges. We have 12 Pentagon’s giving us 60 edges, each is shared by two phases. So that’s 30 does f plus V minus a is equal to well, 12 and 20 or 32 minus 30 equals to the next solid. It’s the last one. The icosahedron you’ve got 30 seconds Shape of each face is an ecological triangle, the number of faces meeting at each vertex is five. The number of faces is 20. The number of vertices, we have 20 triangles that will give us 60 vertices with five faces meeting at each vertex will give us 12. The number of edges, again we have 20 triangles 60 edges, each edge is shared by two phases. So, that’s 30 does f plus V minus equal to 20 plus 12 is 32 minus 30 is two. Next time, we’ll be on page two of the worksheet. We’ll be looking at the volumes and surface areas. But in order to do that, we first have to work out the length of each of the sides of the platonic solids. So that’s the next video. That would be column D on the worksheet.