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cube, trangular prism , cube,
You ask the question as if there were only one possible answer. This is not at all the case, but one example of such a shape is a cube. The unit cell of the triclinic crystal system is another, and there are even less symmetric possibilities (for example, there's nothing in your description requiring the opposite faces to be parallel), but I can't think of any simple name to give them.
triangular pyramid-4 equal faces
It is a polyhedron with two congruent faces: nothing more, nothing less. That can change if several additional conditions are required of the polyhedron.
All triangles have less than 4 lines of symmetry.