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ORIGAMI

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Geometrical origami using A4 paper created by Mitsu Kono

cane-ball
  1. Six-rings cane-ball
     — Sepak tackraw woven ball.
    [Coordinates of the rings]
    (maybe already published somewhere *)
     
  2. Ten-rings cane-ball
     — Kagome ball.
    [Coordinates of the rings]
    [Hexagonal and Octagonal Kagome]
    (You can find numerous ball patterns in Japanese TEMARI. **)
     
  3. ∞(infinity) and Möbius ∞(infinity)
     — Ci and C2 symmetries.
     
  4. Crossed Möbius strips
     — S4 symmetry.
     
  5. Magic cards (XYZ rectangles)
     — Th symmetry.
    (maybe already published somewhere *)
     
  6. Icosahedron propped by the "magic cards".
     
  7. Soccer ball box
     — Two-piece truncated icosahedron.
     
  8. Octagonal cup.
     
  9. Other.
     
* The author was not aware of http://www.geocities.com/mpinaki/origami/strips.html (Yami Yamauchi), http://www.geocities.com/mpinaki/origami/planars.html (Francis Ow), and http://origami.friko.pl/rozne/rozne_wszystkie.php (Kunihiko Kasahara, Extreme Origami, ISBN 0806988533/1402706022).
 
** For example, http://www.temarikai.com/.


Polyhedra made with modular origami units using A4 paper (probably the easiest way) ***

[Coordinates of the vertices of polyhedra]
    polyhedra
  1. Tetrahedron.
     
  2. Hexahedron (cube).
     
  3. Octahedron.
     
  4. Dodecahedron.
     
  5. Icosahedron.

      rhombic dodecahedron and skeletal polyhedra
  6. Rhombic dodecahedron.

     
  7. Skeletal cube.
     
  8. Skeletal octahedron.
     
  9. Skeletal dodecahedron.
     
  10. Skeletal icosahedron.

      soccer ball
  11. Ten-piece dodecahedron.
     
  12. Ten-piece truncated-icosahedron (soccer ball).

     
  13. Sunken icosahedron.

     
  14. Tetrakis hexahedron.

      snub and dual
  15. Snub dodecahedron.

     
  16. Rhombic triacontahedron.
     
  17. Pentakis dodecahedron.
      skeleton
  18. Skeletal cuboctahedron
     
  19. Skeletal icosidodecahedron
     
*** These are designed by the author, but supposed to be the same as some models published somewhere, e.g., http://www.mizushobai.freeserve.co.uk/ (David Mitchell, Mathematical Origami, ISBN 1-899618-18-X) which the author found recently (1/Mar/07).

Origami polyhedra using A4 paper (using single sheet without cutting)

    polyhedra
  1. Quick tetrahedron.
     
  2. Quick cube I.
     
  3. Quick cube II.
     
  4. Quick octahedron.
     
  5. Quick dodecahedron.
     
  6. Quick icosahedron.
     

Classical origami

  1. fusen Paper Balloon (FUSEN).

  2. kabuto War Helmet (KABUTO).

  3. orizuru Crane (ORIZURU).

  4. yakko Footman (YAKKO).

  5. hakama Formal Skirt (HAKAMA). [photo]

  6. ayame Iris (AYAME).

  7. sambo Stand for Offering (SAMBO/SANBO).


Tip

  1. How to make a 30°(π/6) angle.
     
  2. How to make a 36°(π/5) angle. ****
     
  3. How to divide a sheet of paper into equal parts.
     
**** The author's method.

Learn group theory by origami

  1. Point group.
     

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