mario’s company makes unusually shaped imitation gemstones. One genstone had 12 faces and 20 edges. how many vertices did the gemstone have
In a polyhedron, the number of vertices, edges, and faces are related by Euler's formula, which states:
V - E + F = 2
Where V represents the number of vertices, E represents the number of edges, and F represents the number of faces.
In this case, the gemstone has 12 faces and 20 edges. We can substitute these values into the formula and solve for the number of vertices:
V - 20 + 12 = 2
V - 8 = 2
V = 10
Therefore, the gemstone has 10 vertices.