Question 1172379: How many vertices are of a polyhedron having 12 faces and 17 edges?
Answer by ikleyn(52792)   (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.
-----------------
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
|
|
|
