How do you obtain a dodecagon?

[Brimstone]

Is theree a way to obtain an accurate dodecagon from a square or rectangle, doing a single cut?

[origamimasterjared]

Yes.

But why would you want to do it with a single cut? That alone will make it less accurate.

[origamimasterjared]

Inscribed a dodecagon inside a square, and this method came about pretty easily:

[Brimstone]

Thanks Jared. I prefer single cuts because if I have to do a cut for every side (or two), then the points of the eddges will not be whre they have to be.

[Brimstone]

How about a hexadecagon, do you a have a way to make one?

[ahudson]

Pretty much the same, but instead of dividing by three, you divide by four.

[origamimasterjared]

There are two really easy ways based on the same method.

First, is to fold into 4ths instead of 3rds. The cut you make will be different though.

The other method is to pleat into 8ths, then cut like in the dodecagon. This gives you a 16-gon with 4 edges along the edges of the square. It is slightly larger than the 4ths method, but it requires more creases, and skinnier triangles (both leading to increased error).

Too lazy to make a diagram, but here are the plans for both methods:



Edit: in method 1 that cut won't be perpendicular to any existing crease. If it is, you'll just get an octagon. It would be perpendicular to one of the 11.25˚ creases, made by bisecting the angles again.

[Brimstone]

Thanks, I'll try the easy one.