The stars are known by all sorts of names; Folded Paper Stars, German Stars or German Star Ornaments, Swedish Stars, Froebel's Stars, Christmas Stars, Origami Stars, Star Ornaments, Ribbon Star. You'll sometimes see them called Moravian stars; they aren't (that's a different kind of star). In Germany, they were often made of tin. The stars were created, initially, by a German educator Friedrich Fröbel (April 21, 1782–June 21, 1852). Fröbel invented the idea (and the word) behind the modern concept of a kindergarten, and was deeply committed to early childhood education as crucial in the eventual production of well-educated adults. He was keenly interested in, and promoted, the idea of learning via active engagement, and play. The stars were part of that; they actively teach a number of basic geometric and mathematical concepts.
my father. There are all sorts of videos on YouTube showing how to make the stars, as well as instructions about how to make them on the Web; I've linked to a few below. It's a good idea to practice using plain paper first; it can take a bit to get the hang of making the stars. Once you understand the basic method, try using two colors of paper, or try different kinds of points, or using ribbon. I've made stars that were a foot or more across, as well as stars that are smaller than an aspirin. Here's one site about making German stars; here's another that's a downloadable, printable .pdf. Here are two YouTube videos: video 1, video 2.
Star image credit: Kate Ter Haar.