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A square is not a solid figure at all. It's a flat figure, with four congruent faces and four congruent angles.
There is no solid figure with only four edges. The smallest solid figure is the tetrahedron, made up of four triangular faces, but it has six edges.
Tetrahedron
A rhombus is a plane (flat) figure so it has no faces. It has 4 edges and four vertices
A solid with four faces for maths is a tetrahedron.