Surface Area Efficiency Comparison
Just a sample of modular origami surface area efficiency comparisons that I do. This analysis I do on some modulars that result in a completed closed surface to get an idea of how much paper was "wasted" in making locks and getting the right shapes for the particular polyhedron.
The black areas are the portions of each sheet of paper that becomes a part of the surface of the finished model (drawn perfectly to scale). The percents were calculated with a little help from AutoCAD.
As you can see, the sonobe unit is pretty inefficient. Though it should be noted that it sacrifices this efficiency for simplicity and flexibility. The other two are models of mine with both pictures and diagrams in my photostream. They were specifically designed for one polyhedron each, so in the customization allows them to gains efficiency.
Although 26%, or about 1/4 (for the dodecadodeca), might not sound very efficient, the drastically increased complexity of the shape it produces, including points of negative curvature, makes this design pretty efficient for what it does IMO; considering that it's twice as efficient as the sonobe unit.
The Icositetrahedron is one of my most efficient designs. The final model made from 24 sheets of paper is almost TWICE the diameter of a 30-piece sonobe model made from the same sized paper.
A simple example of a modular with even MORE efficiency is the Butterfly Ball, which sacrifices integrity for a 50% efficiency. This model doesn't even really have a lock; it is held together by friction. In fact, technically the sonobe unit is ALSO held together purely by friction, but at least the sonobe unit has pockets instead of just overlapping paper. Both of my designs shown here have strong, mechanical locks not based around friction.
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Surface area efficiency for my truncated rhombic triacontahedron (not shown here) is 30.9%, which I think is pretty good considering the super-strength of the locking mechanism.
Diagrams for all 3 of my models described here, the two in this photo as well as the one I just mentioned can be found in my "Diagrams & Notes" set. Photos of the completed models are in my "Origami Modulars" set.
Surface Area Efficiency Comparison
Just a sample of modular origami surface area efficiency comparisons that I do. This analysis I do on some modulars that result in a completed closed surface to get an idea of how much paper was "wasted" in making locks and getting the right shapes for the particular polyhedron.
The black areas are the portions of each sheet of paper that becomes a part of the surface of the finished model (drawn perfectly to scale). The percents were calculated with a little help from AutoCAD.
As you can see, the sonobe unit is pretty inefficient. Though it should be noted that it sacrifices this efficiency for simplicity and flexibility. The other two are models of mine with both pictures and diagrams in my photostream. They were specifically designed for one polyhedron each, so in the customization allows them to gains efficiency.
Although 26%, or about 1/4 (for the dodecadodeca), might not sound very efficient, the drastically increased complexity of the shape it produces, including points of negative curvature, makes this design pretty efficient for what it does IMO; considering that it's twice as efficient as the sonobe unit.
The Icositetrahedron is one of my most efficient designs. The final model made from 24 sheets of paper is almost TWICE the diameter of a 30-piece sonobe model made from the same sized paper.
A simple example of a modular with even MORE efficiency is the Butterfly Ball, which sacrifices integrity for a 50% efficiency. This model doesn't even really have a lock; it is held together by friction. In fact, technically the sonobe unit is ALSO held together purely by friction, but at least the sonobe unit has pockets instead of just overlapping paper. Both of my designs shown here have strong, mechanical locks not based around friction.
___________________________
Surface area efficiency for my truncated rhombic triacontahedron (not shown here) is 30.9%, which I think is pretty good considering the super-strength of the locking mechanism.
Diagrams for all 3 of my models described here, the two in this photo as well as the one I just mentioned can be found in my "Diagrams & Notes" set. Photos of the completed models are in my "Origami Modulars" set.