The Christmas Star Ornament should preferably not be five pointed (viz. a pentagram) because that happens to be a favorite symbol for devil worshipers, witches, free masonry, etc. It is a symbol of luck for them. Good luck if pointed upward and bad luck (i.e. for a curse) if upside down!
This came to mind when I again saw the ornament on the tree in our parish Church, which happens to be an upside down pentagram. Besides being the ugliest type of star, and in it's ugliest position it also happens to be an occult symbol for the devil himself. It should be replaced by something at least more neutral in cult and more pleasing in form.
N.B. Not all stars are the same. E.g. The star of David, which is a legitimate Christian symbol (of Christ, son of David), has six points (a hexagram).
An eight pointed star (octagram) is perhaps optimal since eight is the symbol of Creation and the Lord's Resurrection (Sunday, the first day of Creation and the Resurrection day, being the eighth day).
Twelve is also very significant in the Judeo-Christian dispensation: twelve tribes of Israel, twelve Apostles, twelve days of Christmas. Notice the Rockefeller Center Christmas Tree Swarovski Star is twelve points (a dodecagram)!
BTW, angels are great tree toppers too, and, to my knowledge, the devil worshipers have not hijacked any of them for their cult. I think they just use fallen angels (devils) in their cult images!