A cube.
The cube has 8 corners and six faces, all of them being squares. The square is a special case of a rectangle, all sides being equal in length. So a cube meets the definition posed in your question.
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A figure that has six rectangular faces is a rectangular prism.
Pyramid: Five faces, eight edges, and five vertices. Prism: Six faces, twelve edges, and eight vertices.
A triangular prism ! It has a triangular face at each end, a rectangular base and two adjoining rectangular faces. It actually has nine edges and six corners.
six faces
six faces