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File: PaperDodecahedron !! The idea ... OK, this is really cool. With just folded paper _ you can make a fantastic looking dodecahedron, _ one of the best looking objects in mathematics. ---- !! How do I do that? Make one "module" ... | images/dodec_0.jpg | So, start with a _ piece of paper _ that's 3x4. _ _ Yes, I know this _ one is 6x8 - work _ with me here ... | | images/dodec_1.jpg | Fold it lengthwise _ into 3, creating _ a Z-fold. | | images/dodec_2.jpg _ images/dodec_3.jpg _ images/dodec_4.jpg | Lay it flat on the table _ as shown here. _ _ Fold all three layers _ together on the dark _ lines. _ _ Fold the top left down, _ the bottom right up and _ fold the diagonal in the _ middle. _ _ All three folds are in the _ same direction - all three _ folds are "upwards". | ---- !! Fit them together ... | images/dodec_5.jpg | Here you can see that _ the short fold at one tip _ matches the long fold on _ the diagonal. | | images/dodec_6.jpg | It gets tucked _ into the gap. _ _ _ This is a _ little tricky. | | images/dodec_7.jpg | We're looking back now _ from the other direction. _ We can see two edges on _ the vertex. | | images/dodec_8.jpg | Here you can _ see the third _ edge being _ inserted. | | images/dodec_9.jpg | This gives you _ one complete _ vertex. | ---- !! Lather, rinse, repeat ... The completed object ... [[[ images/PaperDodecahedron.jpg ]]] There may be a movie to follow ...