Is a prism correct if all of its edges are equal to each other?

If the edges can be equal, but different shapes have the same sides. For example, at the rhombus. A rhombus is not a regular polygon. Since the angles between adjacent sides are not equal. By the definition of a regular prism, we know that there must be a regular polygon at the base. And that’s just one condition. For a correct prism, it is additionally necessary that the side edges are perpendicular to the base planes. In this case, there is not enough data in the problem statement.