they are a polygon
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Opened hexagonal prism.
Hexagonal Prism
yes Sometimes those rectangles could be squares, which are by definition a type of rectangle.
Yes cutting a rectangle in half (either horizontally or vertically) will yield two smaller rectangles (each of which is the same size and shape as the other).
Rectangles are not squares. The reason to this is because squares must have sides of equal lengths. Rectangles are quadrilaterals with sides that join to make 90 degree angles, but are not restricted to having the same length. Therefore "all squares are rectangles", but rectangles cannot be squares.