In mathematics, the binary cyclic group of the n-gon is the cyclic group of order 2n, thought of as an extension of the cyclic group by a cyclic group of order 2.
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 under the 2:1 covering homomorphism
of the special orthogonal group by the spin group.
As a subgroup of the spin group, the binary cyclic group can be described concretely as a discrete subgroup of the unit quaternions, under the isomorphism where Sp(1) is the multiplicative group of unit quaternions. (For a description of this homomorphism see the article on quaternions and spatial rotations.)
Famous quotes containing the word group:
“Now, honestly: if a large group of ... demonstrators blocked the entrances to St. Patricks Cathedral every Sunday for years, making it impossible for worshipers to get inside the church without someone escorting them through screaming crowds, wouldnt some judge rule that those protesters could keep protesting, but behind police lines and out of the doorways?”
—Anna Quindlen (b. 1953)