Certainly, to find the number of vertices in your 16-faced prism, we will use Euler's formula for convex polyhedra. The formula states that, for any convex polyhedron, the number of vertices minus the number of edges plus the number of faces equals 2. It's written as:
Vertices - Edges + Faces = 2
Since we already know the number of faces (which is 16), we can proceed to figure out the remaining values.
In a prism, and according to Euler's formula, it is given that the number of edges equals 3 times the number of faces. This means that the number of edges in our particular prism would be:
3 * 16 = 48 edges
Now we have the number of edges, we can substitute these values into Euler's formula to find the number of vertices:
Vertices = Edges - Faces + 2
By plugging in our values we will get:
Vertices = 48 - 16 + 2 = 34 vertices
Therefore, a 16-faced prism has 34 vertices.