Corrin was a planet that orbited the Sigma Draconis.
Prior to its devastation by atomics, Corrin was a radiation-prone world, due to the red giant status of its star. It was barely habitable to humans, but became a favored location for thinking machines after the rise of Omnius. Indeed, after Earth was reduced to a radioactive husk by the League of Nobles, Corrin became the new location of Omnius Prime.
Role During the Jihad
As a result of the Great Purge Omnius was confined to the planet for several decades, during which time the planet was mined of all its natural resources. It was eventually turned into a radioactive wasteland by the Army of the Jihad during the Battle of Corrin.
Corrin was above all else the name of the space battle near the star Sigma Draconis in 88 B.G. which brought the predecessors of Shaddam IV to the imperial throne. It is said that the victor was one Count Sheuset Ecevit, who took the regnal name of Sheuset Corrino in remembrance of the battle. 
It was in this battle that Abulurd Harkonnen, the lineal ancestor of the evil Baron we love to hate, disgraced himself by an act of cowardice. Others assert that it was in fact an act of treachery. It may be that the House Atreides was first distinguished here by the heroics of Demetrios Atriedes. 
The battle will take its name from a quasi-nebula that was in turn named after the nearby planet Corrin. This quasi-nebula had resulted from the collision of a planetoid with a sub-stellar companion of Sigma Draconis. 
One finds, incidentally, that there were two ancient battles fought at Coroneia in mainland Greece on the road from Thebes to Phocis: The first in 447 B.C.E. saw the defeat of the Athenians by the Boeotians; the second in 394 B.C.E., the nominal victory of Agesilaus II, King of Sparta, over the Thebans and their allies. In the latter battle, Xenophon and others of the legendary Ten Thousand fought on the Spartan side.
Sigma Draconis is relatively close to Old Earth (18.8 ly.)-one might say, in the Sirian Sector. It is interesting that this battle took place so close to mankind's birthplace. The star name of Alsafi is taken from the Arabic Athafiyy, "cooking tripods". (Are we to be reminded of the Death Tripod of the desert executioner?)
It is part of the constellation Draco, the "dragon", which is associated with the obvious mythical monsters, including Tiamat and the dragon which guarded the Golden Fleece.
The alpha star of Draco, called "Thuban", was the Pole Star 4000 years ago (the honor now belonging to Polaris, thanks to the wobble of the Earth's axis). As such, it may have been to this star that the ancient Egyptians aligned some of their temples and pyramids. [Ibid.] Furthermore, the Chinese regarded the stars that revolved around the celestial North Pole and the Pole Star as the heavenly equivalent of their own terrestrial "Middle Kingdom", centered on the Emperor. Perhaps this is why Herbert placed the epochal space battle here.
The Arrakis is also in this constellation, and the Atreides may have their historical origins (ignoring their Homeric genealogical claim) in the Mockmuhl cluster near Upsilon Draconis. And as will be explained, Gamont and Grumman also revolve about a star in Draco.
The Encyclopedist informs us of another planet of Sigma Draconis: Ishkal. The language of this planet provided the word "Shai-Hulud" to the Zensunni ancestors of the Fremen-originally it stood for an extinct but formidable vermiform creature native to Ishkal. [DE, page 236] Since it is not mentioned in the Dune Chronicles, I have not listed it separately but note its putative existence here.
- DE, page 168
- DE, page 56
- DE, page 169
- DE, page 56