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What determines the number of points of symmetry in a 2-mirror kaleidoscope?

Kaleidoscope Points Symmetry
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What determines the number of points of symmetry in a 2-mirror kaleidoscope?

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The number of points of symmetry is determined by the angle between the 2 mirrors. The smaller the angle, the more points of symmetry. For example, mirrors having an interior angle of 30o would have 12-fold symmetry or a 6-point star.

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