The star is named after its inventor, Friedrich Wilhelm August Fröbel (1782-1852). It was conceived as one of many activities for children in Kindergarten (nursery school), another invention of his.
This star is perhaps the most famous of his handicraft constructions, and the net has numerous descriptions of how to fold it, but I think this site would not be complete without one.
According to the wikipedia, it is also known as Advent star, Danish star, German star, Nordic star, Pennsylvanian star, Polish star, Swedish star, and Christmas star in English.
[Note: Most steps are illustrated by more than one picture. The idea was that alternative views would help the viewer understand what's going on. Unfortunately, since 2006, this site has become greedy, and has clamped down on the free viewing of these alternative views. Now you have to pay to see them. Not exactly what I had in mind. They have also "edited" the title of this Instructable, as if I would not know what to call my own instructables. The title should be "Fröbelstern", nothing more, nothing less.]
Step 1: Cut paper strips
It really helps if their width does not wary too much along their length, so if you can get hold a roll of ticker-tape or some other type of pre-cut paper strips, go for it. An office cutting machine is a good option if you have to make your own.
Step 3: Trim the tips
(If you plan to fill a X-mas tree, this step should be possible to throw out once you get the hang of things.)