I came across an interesting website where you can upload any image and it will output a template of the image mapped onto an icosahedron. Above are photographs of two models I created using the website. For the first model I input a satellite image of the entire Earth. For the second I input an image of an 18th century European map of the celestial sphere which shows artistic representations of the constellations. Each model is about 3" across and they were each constructed with cardstock and double sided tape. To try it yourself, go to http://www.hirax.net/map/.UPDATE 5/14/19: Sorry. After 11 years, this feature of the Hirax website is no longer available. :(
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