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A sphere is characterized by a very unique point group known as R3 (Full Rotation Group). A sphere has an infinite number of C2, C3, etc. up to Cinfinity as well as Cinfinite perpendicular axes and an infinite number of mirror planes on every plane and in between each plane. A sphere even has Sinfinity operations and multiple inversion operations. Every symmetry operation known is able to be performed on a sphere an infinite number of times in all directions.

No molecules actually fit into the R3 symmetry group and in fact, only objects, images, and atoms fit into this category.

Sources: Advanced Inorganic Chemistry student

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