no. vertices are corners basically, and edges are edges. Eullers theorem Faces+Vertices=Edges+2.
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7 faces, 7 vertices's, 12 edges.
No edge is like to a cliff but a boundary is like a football field or a basketball court.
4 Verticies, 4 edges
The cone and the pyramid both have a base and a tip. The cone has a circular base and only 2 faces, 1 edge, and 1 vertex. The pyramid can have 4 verticies, 6 edges, and 4 faces; or 5 verticies, 8 edges, and 5 faces.
A cube has 8 verticies {corners} 12 edges and 6 faces