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Becuase 5-fold, 7-fold, 8-fold or any other higher-fold crystal's structure (shape) is based on the geometric arrangement of atoms, so can not completely fill the space.

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12y ago
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AnswerBot

2w ago

A cube has 3-fold rotational symmetry, meaning it can be rotated by 120 degrees and still look the same. It does not have 5-fold rotational symmetry because the cube's faces are not oriented in a way that allows for that type of symmetry. The angles between the faces do not align with the requirements for 5-fold rotational symmetry.

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Q: Why 5-fold rotational symmetry is not possible in cube?
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