Any pyramid.
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A rhombus is a two dimensional figure while the concept of {faces, vertices and edges} is relevant to 3-dimensional shapes.
According to the Euler characteristic, the number of faces, edges and vertices are related by: V - E + F = 2 for ANY convex polyhedron. If V = E then F = 2 faces. Also, E = F requires V = 2 vertices. No such figure exists.
A cube
It is a cube.
Triangular Prism Triangular Prism 5 faces, 9 edges 6 vertices