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It depends on what you mean by "the last time". Your last time may not be my idea of last time.

The turn that brings the object back to its starting position IS counted but only if the object has at least one other position of symmetry. This is to exclude objects that have symmetry of order 1. These are not regarded as being symmetrical because then every object would be symmetrical.

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Q: Why does the last time when you turn a shape for rotational symmetry not count towards the number of times it has rotational symmetry?
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