For this reason the dicyclic group is also known as the "'binary dihedral group"'.

Note that the dicyclic group does not contain any subgroup isomorphic to Dih.

These include the dihedral groups, the quasidihedral groups, and the dicyclic groups.

More generally, given any finite abelian group with an order-2 element, one can define a dicyclic group.

In 1 dimension, the pin groups are congruent to the first dihedral and dicyclic groups:

The stomata are haplocheilic, monocyclic or dicyclic, usually depressed, with the guard cells occurring in the lowermost part of the stoma.

In addition to the powerful hull, the small, squat ship had a very efficient dicyclic warp signature, decades ahead of anything the Malons had developed for faster-than-light travel.

The analogous pre-image construction, using Pin(2) instead of Pin(2), yields another dihedral group, Dih, rather than a dicyclic group.

Coxeter labels these dicyclic groups , being a special case of the binary polyhedral group and related to the polyhedral groups (p,q,r), and dihedral group (2,2,n).

The quaternion group consisting of the 8 Lipschitz units forms a subgroup of index 15, which is also the dicyclic group Dic; this covers the stabilizer of an edge.

In 2 dimensions, the distinction between Pin and Pin mirrors the distinction between the dihedral group of a 2n-gon and the dicyclic group of the cyclic group C.

Since for a cyclic group of even order, there is always a unique element of order 2, we can see that dicyclic groups are just a specific type of generalized dicyclic group.