SOLUTION: How many vertices are of a polyhedron having 12 faces and 17 edges?

Question 1172379: How many vertices are of a polyhedron having 12 faces and 17 edges?
Answer by ikleyn(52793) (Show Source): You can put this solution on YOUR website!
.


Use the Euler polyhedron formula

    F - E + V = 2


(Faces minus Edges plus Vertices equals 2).


Substitute here F = 12  and  E = 17 :

    12 - 17 + V = 2.


You will get then

         V = 2 - 12 + 17 = 7.    ANSWER

Solved, answered and explained.

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About Euler polyhedron formula, see this articles

http://www.ams.org/publicoutreach/feature-column/fcarc-eulers-formula#:~:text=This%20theorem%20involves%20Euler's%20polyhedral,%2B%20F%20%2D%20E%20%3D%202.

https://plus.maths.org/content/eulers-polyhedron-formula

https://en.wikipedia.org/wiki/Euler_characteristic

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