Mario's company makes unusually shaped imitation gemstones. One gemstone had 12 faces and 20 edges. How many vertices did the gemstone have?
a) 34 vertices
b) 10 vertices
c) 30 vertices
d) 8 vertices
Let V be the number of vertices.
According to Euler's formula, V - E + F = 2, where E is the number of edges and F is the number of faces.
Since the gemstone has 12 faces and 20 edges, we have:
V - 20 + 12 = 2
V = 10
Therefore, the gemstone has 10 vertices, and the answer is (b) 10 vertices.