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To determine the number of different rectangular prisms that can be made using exactly 12 cubes, we need to find all the possible combinations of dimensions that result in a volume of 12. The factors of 12 are 1, 2, 3, 4, 6, and 12. Each factor represents a possible dimension for the rectangular prism. Therefore, there are 6 different rectangular prisms that can be made using exactly 12 cubes.
There are many options: 2 rectangular prisms 2 cubes 2 parallelepipeds 2 tetrahedrons 2 square based pyramids are some possibilities using convex polyhedra.
Probably infinite. The smallest is known as Ramanujan's number, 1729 using cubes of 1 and 12, and of 9 and10. Read more about the genius Ramanujan in Wikipaedia.