Platonic Solids Cont...


    Now that you have filled out the chart on the previous page, let's explore a couple of formulas which may stream line the process of counting faces, edges, and vertices.
    In the first formula, we will allow V to be total number of vertices of the solid.  F to be the number of faces, J to be the number of vertices of each face, and L represents the number of faces at each vertex.

    Notice that with a tetrahedron, there are 4 faces, 3 faces at each vertex, and each face has 3 vertices associated with it.  Therefore, F = 4, J = 3, and L = 3.  

    According to our formula, we find that the total number of vertices of a tetrahedron can be found with:

V=(3*4)/3 = 4

    Therefore, a tetrahedron has 4 vertices.

    



    If there is a nice way to calculate the number of vertices that our solids have, maybe there is a nice way to calculate the number of edges our figures have.  This is my challenge to you.
 
  1. Derive a formula which will find the number of edges of a polyhedron of the type we have explored in this unit.
    (Hint:    Use the previous formula to help you.)
    Write your answer on a piece of paper.  Justify why your formula works, and provide an example to show that it does work.  Turn this paper into your teacher when you have completed this part of the assignment.  The correct answer will be provided to the class at a later date.


 

End of unit questions