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Rectangular pyramids and triangular pyramids both have triangular faces.
They both have sides that are rectangular in shape. They both have a constant cross-sectional shape equal to the shape of the ends (triangle for a triangular prism; rectangle for a rectangular prism).
They are both polyhedra with five faces.
A cuboid (rectangular prism) is the only shape with 6 rectangular faces (3 pairs of rectangles in fact). A cube is a special type of cuboid where all the rectangles are squares. Both cubes and cuboids are special types of hexahedron (polyhedrons with 6 faces). The only shape with 6 equal rectangular faces is the hexagonal prism. However, since it also has two hexagonal faces it is therefore an irregular octahedron rather than a hexahedron.
They both have a triangular shape