Oschene's Octahedral Dib's Box

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    Here is my solution for constructing Oschene's Octahedral Dib's Box without printing the CP. You will still need to find a way of obtaining a circle of paper though.

    See his original CP here: www.flickr.com/photos/oschene/4609233017/
    And model here: www.flickr.com/photos/oschene/4609246357/

    Step Instructions:
    1. Mark the center.
    2. Bring any point from the edge to the center and pinch sides.
    3. Bring one pinch to the center and pinch as shown.
    4. Pivot around the same pinch to bring another edge-point to the center, and pinch as shown.
    5. Make the bold creases, starting with the one that almost goes through the center.
    6. Mark the midpoint of this crease as shown.
    7. Use the previous mark as reference for these 3 creases.
    8. Finish the CP.

    To collapse, reference Oschene's original CP for the mountain/valley designations.

    oschene, mimickr, Origami Natan, and 6 other people added this photo to their favorites.

    1. oschene 59 months ago | reply

      Brilliant -- and entirely different from the method I was ruminating. The intersection in step four is intriguing. Looking forward to trying this out.

    2. Daniel Kwan 59 months ago | reply

      Actually, based on your description from before, this method is based on the same idea. Note that the angle between the biggest chord in step 5 and the incomplete fold in step 2 is your arctan(√3/5).

      It helps in understanding this method if you realize that all of those pinch-marks lie on an inscribed star-of-david. Then, you can see through similar triangles (one drawn on the star-of-david grid, and one drawn on the final grid), that the angle at step 5 is correct.

    3. Daniel Kwan 59 months ago | reply

      I just realized that probably a more practical method of finishing the grid after step 5 is to use that new edge-point to mark the last 2 points on the edge of the circle (by pivoting around it to bring points on the edge to the center, and pinching on the other side). This would probably greatly reduce folding error. When I made the choice for step 6 I was thinking from a minimalist's perspective.

    4. oschene 59 months ago | reply

      Folded it twice this morning on the bus. I initially had some trouble get the parallel crease in 7 to be accurate, but the second time, it came out better. Great fun to be trying to puzzle out diagrams to a model I knew already.

      I can't quite visualize what you're suggesting in your second comment. Could you draw me another circle?

    5. origami_madness 59 months ago | reply

      I'm probably grabbing at straws here, but the juxtaposition of the triangle grid on the largest possible triangle reminds me somewhat of this photo. Is there anything going on here, or am I just seeing things?

      This construction also happens to divide the diameter of the circle into tenths, btw.

    6. Daniel Kwan 59 months ago | reply

      Oschene: Glad it worked for you! I'll make you a replacement steps 6-8 in a bit.

      Madness: You're not ENTIRELY crazy. When I started porting my square tessellation ideas to triangle grids, I discovered you can use the same "slope" tricks. Obviously on a triangle grid, since I would usually count grid-distances which are not perpendicular to one another, it may not technically be "slope"... but it works with the same underlying principle of similar triangles.

      This solution is to some extent an application of that concept... So yes, this is a somewhat distant relative of what is in that other photo.

      And wow, I had not noticed that this provided a division of the circle into 10ths... Good find =) This kind of thing happens a lot with slope-stuffs.

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