There are many possible answers:
Any one of the four larger Platonic solids (not the tetrahedron).
In all cases, moving one of the faces laterally will still leave a solid which will beet the requirements : the cube (hexahedron) could become a rhombohedron.
There are many more shapes with fewer symmetries.
A cylinder
A prism.
A cylinder would fit such a description of it.
The two parallel and congruent faces of a solid are called bases. In three-dimensional geometry, these bases can serve as the top and bottom faces of shapes like prisms and cylinders. The congruence and parallelism of the bases are key characteristics that define these solids.
Most things do not have two congruent parallel bases. I do not, by desk does not, my lap top does not, etc etc.
Both a cylinder and a prism can have parallel and congruent bases.
An upright pentagonal prism has two congruent parallel bases and 15 edges.
cylinder
A cylinder
A prism has two congruent parallel bases.
Prism!
A prism.
A cylinder would fit such a description of it.
parallelogram, because if the two bases are congruent and parallel then the sides will also have to be parallel, so it is a parallelogram
The two parallel and congruent faces of a solid are called bases. In three-dimensional geometry, these bases can serve as the top and bottom faces of shapes like prisms and cylinders. The congruence and parallelism of the bases are key characteristics that define these solids.
Most things do not have two congruent parallel bases. I do not, by desk does not, my lap top does not, etc etc.
Sounds like a rectangular solid to me, such as an elongated box.