How many symmetry planes does a 4D hypercube have?

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How many symmetry planes does a 4D hypercube have? For the square and the cube, there are two types of symmetry lines or planes, the orthogonal ones and the diagonal ones. In n dimension there will be n orthogonal symmetry planes I think, but I'm not sure about the diagonal ones. For the cube, each diagonal symmetry plane is determined by an edge, so one only needs to count the edge and divide it by two since each plane contains a pair of edges. But in four dimension I have trouble visualizing what a plane looks like. If it looks like a cube, then it has 12 edges...