Example to Verify Euler’s Law:

check out Euler's law for the following parts shown below 

Solution

 (a)       We see Figure (a) that the part has nine edges, five faces, & six points.

        By according to Euler's law we have

                               F - E + V = 5 - 9 + 6 = 2

that satisfies Euler's rule.

(b)        We suppose that two cylinders are approximated by two cubic holes.

By according, the part in Figure (b) has 54 edges (12 edges for the pocket, 12 for each cubic hold equivalent to a cylinder, 18 in the outside boundary of object), 21 faces, & 36 vertices (three or more than three intersecting lines explained a vertex), 5 inner loops (i.e., four end loops of the two holes & one loop of the bracket), 1 body, and 2 genuses (the two holes). Thus, from Euler's rule we have

F - E + V - L = 21 - 54 + 36 - 5 = - 2

2 (B - G) = 2 (1 - 2) = - 2

That satisfies Euler's rule.