A square prism and a cube are related shapes, but they are not the same thing. Let’s break down the definitions to understand their differences.
A cube is a specific type of prism that has all its faces as squares. This means that a cube has equal edge lengths, and each of its angles is a right angle. Overall, a cube has 6 faces, 8 vertices, and 12 edges, and because each of its faces is a square, every side is the same length.
On the other hand, a square prism is a three-dimensional shape that has two square bases and four rectangular sides. While the bases are square, the sides can vary in length, which means that a square prism can have rectangles as its lateral faces. Because of this, a square prism does not require that all edges be of equal length; only the edges that form the bases need to be. Therefore, a square prism can be taller or shorter depending on the height of the rectangular faces connecting the two bases.
In summary, while all cubes are square prisms (since they have square bases), not all square prisms are cubes. The key difference lies in the lateral faces and the uniformity of the edges. A cube is a particular instance of a square prism with equal-length edges and square faces, while a square prism can have varying heights that create rectangular lateral faces.