The analogous pre-image construction, using Pin + ( 2 ) instead of Pin & minus; ( 2 ), yields another dihedral group, Dih 2 " n ", rather than a dicyclic group.
12.
In 2 dimensions, the distinction between Pin + and Pin " mirrors the distinction between the dihedral group of a 2 " n "-gon and the dicyclic group of the cyclic group " C " 2 " n ".
13.
The dicyclic group is a binary polyhedral group it is one of the classes of subgroups of the Pin group Pin & minus; ( 2 ), which is a subgroup of the Spin group Spin ( 3 ) and in this context is known as the "'binary dihedral group " '.
14.
The smallest abstract groups that are " not " any symmetry group in 3D, are the quaternion group ( of order 8 ), Z 3 & times; Z 3 ( of order 9 ), the dicyclic group Dic 3 ( of order 12 ), and 10 of the 14 groups of order 16.
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