Borg Queen's vessel

The Borg Queen's vessel was a unique, octahedron-shaped starship that was used by the Borg Queen to travel. Little was known about its capabilities or specific purpose, except that the only Federation encounters with this starship design were when the vessel was used to transport the Queen. The ship was heavily armed, well protected, and, like all Borg ships, capable of transwarp speeds.

The vessel was present when Species 10026 was assimilated in 2375; Seven of Nine and the Borg Queen were aboard while this assimilation took place. Later, the vessel pursued the Delta Flyer when it escaped from the Unicomplex after rescuing Seven. The vessel was destroyed when the USS Voyager collapsed the transwarp conduit it was traveling in. 

Background information
No designation was formally given for this starship design. The script of "Dark Frontier" describes it merely as "massive" and "a complex, distinctive geometric shape we've never seen before." It remains unknown whether any other ships of this type exist.

The diamond-shaped vessel designed by Dan Curry, and whose design was translated into a CGI model by Brandon MacDougall. (Cinefantastique, Vol. 31, No. 11, p. 33)

Apocrypha
According to the video game Star Trek Armada (and many other games), this ship class is referred to as a "Borg diamond," due to its shape and the fact that it follows the naming conventions used in describing the cube and sphere (though if the naming convention is properly adhered to, "Borg octahedron" is the more applicable designation).

In Star Trek Online, the Borg Queen commands a vessel of this class, termed the Borg Queen's Octahedron, during Battle Group Omega's assault on the new Unicomplex in the Gamma Orionis Sector Block.