Octagonal unit with star was described by Tomoko Fuse in her "Unit origami" (Tomoko Fuse, Unit Origami. Multidimensional Transformations, Japan Publications Inc., Tokio and New York 1990, ISBN 0-87040-852-6) . She used this module to build a truncated cube. A module itself is nice, specially when folded from gift wrapping paper.
If you use geometric pattern papet you obtain Chrismas star effect.
The same paper (shown above) is used to fold all stars shown below. The difference is the size of the square of paper (1 grid x 1 grid for smal stars, 2 grids x 2 grids for large stars). The paper is cut paralel to pattern or 45 degrees to pattern. In one case the cut passes through center of the big red square, in the other case the cut overpasses between dark belts. You can see the effects below:
Here you can see another pattern of the paper and stars folded from this paper.
One more paper and results of its folding.
And more...
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