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In mathematics, the binary cyclic group of the n-gon is the cyclic group of order 2n, C 2 n {\displaystyle C_{2n}} , thought of as an extension of the cyclic group C n {\displaystyle C_{n}} by a cyclic group of order 2. Coxeter writes the binary cyclic group with angle-brackets, ⟨n⟩, and the index 2 subgroup as or.
It is the binary polyhedral group corresponding to the cyclic group.
In terms of binary polyhedral groups, the binary cyclic group is the preimage of the cyclic group of rotations {\displaystyle C_{n}<\operatorname {SO} } ] under the 2:1 covering homomorphism
of the special orthogonal group by the spin group.
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