The Star of the North, sometimes called the Star of the Dunedain has been steeped in some controversy due to the number of points of the Star being in contention. It is described as being worn by Aragorn and later by the Grey Company or Rangers of the North, of whom Aragorn was the hereditary leader or Chieftain.
They are described thus, "A little apart the Rangers sat, silent in an ordered company armed with spear and bow and sword. They were clad in cloaks of dark grey and their hoods were cast now over helm and head. Their horses were strong and of proud bearing but rough haired. There was no gleam of stone or gold, nor any fair thing in all their gear or harness; nor did their riders bear any badge or token, save only that each cloak was pinned upon the left shoulder by a brooch of silver shaped like a rayed star."
Lord of the Rings, The Passing of the Grey Company
Aragorn himself wore such a Star, hence giving him the name "Thorongil" or "Eagle of the Star".
Concerning the number of "rays" there has been much confusion. Some have said it had six, some five, some even seven or eight. Some of this confusion comes from Robert Foster's book "The Complete Guide to Middle Earth - a lovely tome but one that has some inadvertent errors in it. Foster had used as a reference an early version of The Lord of the Rings in which the publisher erroneously published this information. It wasn't corrected until the publication of Indo's 50th Anniversary Edition. In the Scull and Hammond index under Elendil it says:
"emblems of ( Seven Stars of Elendil and his Captains, had five rays, originally represented the single stars on each of the seven ships (of 9) that bore a palantir; in Gondor the Seven Stars were set about a white- flowered tree, over which the Kings sat a winged crown)"
Also of note, on the original cover of The Return of the King, as drawn by Tolkien himself, the Stars all have five points.