Mario's company makes unusually shaped imitation gemstones. One gemstone had 12 faces and 20 edges. How many vertices did the gemstone have?

Question

a) 34
b) 10
c) 30
d) 8

Answer 1

Let V be the number of vertices in the gemstone.

According to Euler's formula,

V - E + F = 2,

where E is the number of edges and F is the number of faces.

In this case, E = 20 and F = 12. Plugging these values in the formula and solving for V, we get:

V - 20 + 12 = 2
V - 8 = 2
V = 10

Therefore, the gemstone has 10 vertices. The answer is (b) 10.