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

34 vert.
10 vert.
30 vert
8 vert.

Question

Mario’s company makes unusually shaped imitation gemstones. One gemstone had 12 faces and 20 edges. How many vertices did the gemstone have?

34 vert.
10 vert.
30 vert
8 vert.

anonymous · Answer

Have you use Euler's Formula before?

anonymous · Answer

once or twice but I'm not sure exactly what it is

anonymous · Answer

http://www.mathsisfun.com/geometry/eulers-formula.html

anonymous · Answer

But hows that work when I don't have the number of vertices? I put it in as x and solve the equation?

anonymous · Answer

So for any convex polyhedron, the relationship between the Edges, Vertices, and Faces is given by:$$\bf F+V-E=2$$Substitute for the already given number of faces and number of edges and solve for the number of vertices:$$\bf 12+V-20=2 \implies V=?$$

anonymous · Answer

Oh, ok! I'll so that right now

anonymous · Answer

*do

anonymous · Answer

And you understand what convex means right?

anonymous · Answer

I got 10 vertices =D Isn't convex smaller then 180? Or is that 360?