As far as I can make out, none.
According to the Euler characteristic F + V = E + 2 for a 3-D polyhedron where
F = number of Faces
V = number of Vertices
E = number of Edges
If F=V=E then the Euler characteristic implies that F=V=E=2
But you cannot have a solid object with 2 faces.
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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 square has 4 equal sides and 4 vertices of 90 degrees
A prism with an n-sided base will have 2n vertices, n + 2 faces, and 3n edges. That's a cube.
any form of cuboid if the edges were equal, a cube
A cube.