3D star origami

Well, maybe not quite "origami", since there's some gluing involved, but in this article I tell you how to make 3D stars (star polyhedra) with a minimum of effort. Materials and tools needed: paper sheets, scissors, glue, tape.

 The image above is a star dodecahedron which, despite its complex appearance, is quite easy to make following the method I tell you below. You need one and a half sheets of 8.5x11 inch paper to make it (or six sheets, if you want it twice the size).

1. Take the sheet and split it into four equal rectangles. Split the half sheet into two, for a total of six rectangles.
2. Fold each rectangle in half along the major axis, then fold again by the half, so you get this:
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3. Starting from the center of the free edge, fold a corner so that the angle left between its edge and the center is half of the angle between the edge and the crease, as seen below:
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4. The purpose of the previous step was to make a 36 degree angle, which will be the tip angle of the points of the star. If you did it correctly, you can fold it again, and yet again, so there are five angles of the same size, as seen below. If you didn't quite make it, go back to the previous step and adjust the angle a bit until it works.
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5. Now come the scissors. Set the paper as in the figure below and cut it as indicated. When you open it, it should look as in the other picture.
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6. To make a point for the star, put a piece of tape to join two edges, as shown below. We get two points of the start from each piece of paper, attached by one of the sides. There should be some tabs on the free edges, so we can glue the points to each other.
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7. After you've made six sets of two points, you're ready to assemble them into a star. Join star pairs by putting some glue on the tabs and pressing together. It doesn't really matter what pattern you follow, since the star will close in on itself as you build it. To glue the last few tabs, it is useful to use tweezers (the flatter, the better) and squeeze them in the space still available.
8. And behold! There is the star.

If you want to make the eight-pointed star of the picture below, use eight rectangles and change step 3 so that the edge ends up past the centerline, and the angle is split into three instead of five parts. The rest of the steps work the same way.

There's three kinds of regular stars, having four (3-sided, start from a 5-sided point and fold in the unneeded faces), six (4-sded), and twenty (3-sided) points. And there are lots of irregular stars, combining 3-, 4-, 5- and 6-sided points. Can you discover them all?