Problem $3(8$ points$)$

The CWRU math department has discovered a new polyhedron! Unfortunately, they only know

the number of edges, the number of vertices, and that each face is the same shape. They want

you to write a code that can determine how many faces it has. According to Euler's polyhedron

formula, if you are given the number of vertices $(V)$ and edges $(E)$ of any polyhedron you can

determine the number of faces $(F)$ it has. The relationship between these is as follows:

$V-E+F=2$

The data for the mystery object and other polyhedrons has been put in a file named

HW$12\_$Polyhedrons.txt$.$ Read in the data using fscanf, skipping over the string data

without storing it$,$ but storing the vertex and edge data in vectors. $($We will address how to

properly store string data in the next lecture.$)$ Calculate the number of faces each polyhedron has

and store those in a new vector.

Next write the information, plus a statement about the number of faces that the mystery object

has to a new file called HW$12\_$PolyFaces.txt$.$ Use fprintf statements. Instead of

printing the names of the objects, just give them a number, with the last object being the mystery

object. Your file format should look like the example on the next page, though your spacing may

be a little different.

Note that the alignment of the file will probably be a bit off, something like in the example

above, and this is OK$.$ Also note that you can use $\frac{\frac{?}{?}}{t}$ in a fprintf statement to put in a tab.