It can, but only if it a right triangular prism one of whose faces exactly matches the face of the square.
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First of all, it's polygon, not polgon. Second of all, a cube is not a polygon. A polygon is a two-dimensional shape. A cube is a form of a prism. A prism's suffix is hedron.That means that a cube is a hexahedron, according to the number of sides. Though many people think of a hexagon when they hear that, it is disregarding the 'shape' hexagon. A hexagon has six sides, right? Well, a 3 dimensional cube has six sides as well, therefore it would be a hexahedron. The proper name for any given prism would be polyhedron. Not polygon. Thank you for your question.
Yes, but only if one face of one prism is congruent to a face of the other.
A hexahedron in the form of a triangular bipyramid: two triangular pyramids stuck together.
Make an hexahedron in the form of a triangular dipyramid. See link for images.
Any. You can have a triangular pyramid (tetrahedron), a rectangular one, a pentagonal one, and so on. Similarly, you can have a triangular prism, a rectangular prism, and so on.