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What are the symmetries of a cube?

Updated: 4/27/2022
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16y ago

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From the perspective of a symmetry group, a cube has 48 symmetries total. They include:

  • 24 rotational symmetries:
    • the identity
    • 6 90° rotations about axes through the centers of opposite faces
    • 3 180° rotations about the same axes
    • 8 120° rotations about the space diagonals connecting opposite vertices
    • 6 180° rotations about axes through the centers of opposite edges
  • 24 reflection symmetries that involve one of the above rotations, followed (or, equivalently) preceded by the same reflection
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16y ago
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Q: What are the symmetries of a cube?
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