profiles that are square and rectangular
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no, but a cube is a rectangular prism... Remember this, a square is a rectangle but a rectangle is never a square!
square
Square
A rectangular pyramid has a rectangular base and four triangular faces that meet at a single point called the apex. A square pyramid, on the other hand, has a square base and four triangular faces that meet at a single point. The key difference is in the shape of the base - rectangular pyramid has a rectangular base, while a square pyramid has a square base.
One difference is square pyramids have 4 triangular faces while rectangular prisms have none!