How to Find the Vertex

Step-by-Step Guide

1. 1

   Step 1: Learn Euler's Formula.

   Euler's Formula, as it is used in reference to geometry and graphs, states that for any polyhedron that does not intersect itself, the number of faces plus the number of vertices, minus the number of edges, will always equal two.Written out as an equation, the formula looks like:
   F + V
   - E = 2 F refers to the number of faces V refers to the number of vertices, or corner points E refers to the number of edges
2. 2

   Step 2: Rearrange the formula to find the number of vertices.

   If you know how many faces and edges the polyhedron has, you can quickly count the number of vertices by using Euler's Formula.
   
   Subtract F from both sides of the equation and add E to both sides, isolating V on one side.
   
   V = 2
   - F + E , All you need to do at this point is to plug the number of sides and edges into the equation before adding and subtracting like normal.
   
   The answer you get should tell you the number of vertices and complete the problem.
   
   Example:
   For a polyhedron that has 6 faces and 12 edges...
   
   V = 2
   - F + E V = 2
   - 6 + 12 V =
   -4 + 12 V = 8
3. 3

   Step 3: Plug the numbers in and solve.

Detailed Guide

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