For the crease patterns I've chosen, there are three categories as mentioned before:
- Pleats
- Helixes
- S-curves
PLEATS
Above is the crease pattern for the 32-sided tato with my added annotations showing the basic math and method to modify pleated crease patterns. Click on it to see a larger image.I'll summarise the method here. Basically you have your circle, then you divide it into the number of pleats you want. Decide how big you want the base to be, the height, and length of pleats. Then in the height area choose whichever bottom corner of the section you prefer and draw a perpendicular line up to the top of the height area. When the line hits that point, begin your new line and bring the end of it at the division of a segment you drew up in the first step at the edge of the circle.
To understand the math in pleating a total of five crease patterns were studied to find the similarities to help figure out the math behind it. Pictures of the folded models can be found in my previous blog. I used Philip Chapman-Bells' 32-sided tato (Chapman-Bells, 2008), 17-sided tato (Chapman-Bells, 2008), pentagonal petal tato (Chapman-Bells, 2009), and octagonal tato with modified bottom. (Chapman-Bells, 2008) I used an octagonal tato box crease pattern from Jorge Jaramillo to study pleats as well. (Jaramillo, 2009)
I found the Chapman-Bells models to be the most comprehensive in understanding the math. The 32-sided, 17-sided, and Jaramillo's octagonal tatos are "standard tatos". This is where I figured out the basic math for it and from the pentagonal petal and Chapman-Bells octagonal tato with modified bottom with the modifications helped me understand how to add modifications to standard designs. This understanding of I believe would help me greatly in creating my own modifications. I also found that with tatos, if you stick your finger in it your finger gets trapped inside. I think this is fun, and the box could be turned into a simple finger trap. The reason why it can trap fingers is because the flaps are arranged in tangents around a point (radial geometry) and they point downwards slightly. So it works like the arrangement of eel's or shark's teeth where it's easy to get it, but difficult to get out.
HELIXES
This is the crease pattern for the octagonal helix which was the best for understanding on how to create a helix structure with paper.I understand how to modify it, but it's hard to put it in to words. Here's an attempt at putting it in to words. Decide how many layers you want in the helix as well as how many sections, the angle of the layers and helix as well, and the diameter of the helix. Make the collapse area first and on one side link the straight lines to layer angles and helix angles on the other side. Do the same thing with the diagonal but opposite to the straight line. So if on one side The straight line is connected to a layer angle you have the diagonal connection to a helix angle. Add in horizontal lines according to how many layers you need and finish off by adding in the top and bottom sections.
For helixes only two crease patterns were studied. Both are Chapman-Bells' models. One is a one layer helix (Chapman-Bells, 2007), and the other is a multi-layer octagonal helix (Chapman-Bells, 2006).
My favourite thing about these is that they can compress into very flat shapes which makes them wonderful for space-saving.
S-CURVES
For S-curves I used the crease pattern for the onion to understand how they work.It was easier to work out than I thought it would be. They work very much like how pleats do. Basically before you get you straight line at the division you can control your curve to be as extreme/curvy as you want as long as it stays inside its own sector.
As for S-curves I thought they would be harder to figure out so included is a bowl which uses various S-curves. (Chapman-Bells, 2007) The model above, which is the onion, is the main one that helped me understand the construction of S-curves. (Chapman-Bells, 2008) Others also used to understand S-curves are the smart waterbomb (Chapman-Bells, 2007), and seven-sided tato box with curves. (Chapman-Bells, 2008)
They have a lovely, sleek aesthetic look about them.
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Chapman-Bells, P. (2006). The Octuple Helix Compass Rose Jar. Retrieved August 30, 2011, from http://origami.oschene.com/archives/2006/03/11/the-octuple-helix-compass-rose-jar/
Chapman-Bells, P. (2007). Lead Foot Melvin and the Smart Waterbomb. Retrieved August 30, 2011, from http://origami.oschene.com/archives/2007/03/24/lead-foot-melvin-and-the-smart-waterbomb/
Chapman-Bells, P. (2007). Peppermint Drop Bowl. Retrieved August 30, 2011, from http://origami.oschene.com/archives/2007/06/01/peppermint-drop-bowl/
Chapman-Bells, P. (2007). The Spiral Data Tato -- A Curiously Complex Origami CD Case. Retrieved August 30, 2011, from http://www.instructables.com/id/The-Spiral-Data-Tato----A-Curiously-Complex-Origam/
Chapman-Bells, P. (2008). 7-Sided Tato Box, Open Top and S-Curved Sides. Retrieved August 30, 2011, from http://origami.oschene.com/cp/7-tato-box-open-top-with-curves1.pdf
Chapman-Bells, P. (2008). 32-Sided Tato Box. Retrieved August 30, 2011, from http://origami.oschene.com/cp/32-sided-tato-box-straight-sides.pdf
Chapman-Bells, P. (2008). Eight-sided Tato Box, Stackable. Retrieved August 30, 2011, from http://origami.oschene.com/archives/2008/02/13/beaver-dams/
Chapman-Bells, P. (2008). Meditation XVII Box. Retrieved August 30, 2011, from http://origami.oschene.com/archives/2009/01/11/with-apologies-to-mr-ekiguchi/
Chapman-Bells, P. (2008). Onion. Retrieved August 30, 2011 from http://www.box.net/shared/uqzdegu684
Chapman-Bells, P. (2009). Kaki Self-Lock Pentagonal Tato Box. Retrieved August 30, 2011, from http://www.flickr.com/photos/oschene/3206757676/in/photostream/
Jaramillo, J. (2009). Petal Box CP. Retrieved August 30, 2011, from http://www.flickr.com/photos/georigami/3193396658/
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