Things to know:

• Vertices have to go at crossings and at endpoints. You are also allowed to put in extra vertices to split an edge into two edges.
• Edges go between veritices. They are squiggly and sometimes zig-zaggy lines. Edges always start and end at vertices (though sometimes they can start and end at the same vertex.
• Regions are the connected bits of the plane left over after you draw in the Vertices and edges. The outside part is always a region. Don't forget to count it.
• The Euler Characteristic (sometimes called the Euler number) is found by calculating V-E+F. When you do this calculation for a connected set of vertices and edges in the plane, you always get 2!

Practice problems

Count the Vertices, Faces and Edges of each of these, and then calculate the Euler Characteristic/Euler number from the numbers you counted (verify that the Euler number is 2)

Go on to hints on the practice problems