Triangular prism
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A triangular prism has 5 faces, 9 edges and 6 vertices
A rectangular pyramid has 5 faces: a rectangular base, and 4 triangular faces.
A prism *always* has 2 bases. In case you meant "faces" instead of "bases", the prism with the smallest number of faces is the triangular prism - which has 5 faces. If there were any fewer number of faces, the prism which become a two dimensional object.
It is a triangular prism
A triangular prism always has 5 sides. It has two triangular bases and 3 rectangular faces. If the bases are not congruent it is called an oblique prism.