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How many planes and axes of symmetry does a regular octahedron have?

April 26, 2017Axes Mathematics octahedron Planes regular Symmetry

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How many planes and axes of symmetry does a regular octahedron have?

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This is a toughie! I believe there are 9 non-redundant planes of symmetry – one going through the midpoint of each opposite pair of sides (6) and one going through each set of 4 vertices (lengthwise, widthwise, and heightwise – 3). If an axis of symmetry is defined as one about which there is reflexive symmetry, OY. There are lots of them… 3 for the vertices (one through each opposite pair), 4 for the faces (1 through the center of each opposite face), 6 for the edges (1 through the center of each opposite edge), making a total of 13… I think. I don’t believe any of the weird diagonals produce symmetry.