yes, vertices are just about the same thing as edges.
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no numbers have the same number of edges and vertices
no. vertices are corners basically, and edges are edges. Eullers theorem Faces+Vertices=Edges+2.
A cube and a regular octahedron have the same number of edges, vertices, and faces. Both have 12 edges, 8 vertices, and 6 faces.
2 faces can't share the same face, and they cannot share ALL vertices and edges either
The same numbers as for a cuboid. Edges = 12 Vertices= 8 Faces = 6