Question

for the figure, find v + f - e, where v, e, and f stand, respectively, for the number of vertices, edges and faces. v + f - e =

Explanation:

Step1: Count the vertices

By observing the figure, we can see that the number of vertices $V = 10$.

Step2: Count the edges

Counting the line - segments, we find that the number of edges $E=15$.

Step3: Count the faces

Counting the flat surfaces, we get the number of faces $F = 7$.

Step4: Calculate $V + F-E$

Substitute the values into the formula: $V+F - E=10 + 7-15$.
$10+7 - 15=2$.

Answer:

$2$