The crease patterns below all have the property that, when folded up,
a single complete straight cut can simultaneously cut all the bold lines
and no more, producing the desired shape or shapes.
For more information, refer to the page on
the fold-and-cut problem and its mathematics.
These examples were designed by
Erik Demaine and
Martin Demaine.
How To Print
There are three main ways to print these figures, ranging from easiest to
highest quality:
- You can use your webbrowser to print the images at 72 dpi.
The lines will be grainy, but printing this way is the easiest.
- To get higher quality, save one of the high-resolution images (150 dpi
or 300 dpi) to a file, open it with an image viewer, and print it scaled
down to fit to the page.
- To get prefect quality, use the PDF or Encapsulated PostScript versions.
Print to fill the entire page.
If you don't know how to print these files with your printer, see
my information on file formats.
How To Fold
The examples below all follow the following notation:
- Bold lines are the desired cuts. Usually these lines are solid,
and you should not fold along them.
- The thin outside rectangle is intended to be the boundary of the paper.
After printing, you can cut the paper to those limits,
although this is mostly unnecessary.
- The dashed lines are "valley" folds, and should be folded "towards" you.
- The dot-dashed lines are "mountain" folds, and should be folded "away"
from you.
- Some of the examples have a middle line of symmetry. Mountain fold
along such a line before you do anything (including precreasing).
To make one of these examples, here is one recommendation procedure,
depending on your expertise in folding crease patterns:
- Print the crease pattern as large as possible, and possibly also
photo-enlarge using a photocopier onto larger paper.
- Precrease all the creases (dashed and dot-dashed) by pinching the paper
and making sure that you follow along the printed lines.
This may get your hands a little dirty with toner.
- Reverse the valley (dashed) creases, so that all crease have their
proper orientation.
- Now the hard part: collapse all the creases simultaneously.
This can take some practice, especially on the harder examples,
but with some effort you should be able to get it.
Straight Skeleton Method
These examples are all based on the
straight-skeleton solution
to fold-and-cut, because this method typically produces practical foldings.
The foldings can be made even more practical (as in several of the examples
below) by slightly perturbing the graph of desired cuts so that multiple
edges of the straight skeleton align to produce high-degree straight-skeleton
vertices and fewer straight-skeleton edges and creases overall.
MIT Logo
[PDF]
[Encapsulated PostScript]
[36 dpi image (shown)]
[72 dpi image]
[150 dpi image]
[300 dpi image]
Thanks to Nina Strohminger for finding a good folding of this model.
Swan
[PDF]
[Encapsulated PostScript]
[72 dpi image (shown)]
[150 dpi image]
[300 dpi image]
Angelfish
[PDF]
[Encapsulated PostScript]
[72 dpi image (shown)]
[150 dpi image]
[300 dpi image]
Butterfly
[PDF]
[Encapsulated PostScript]
[72 dpi image (shown)]
[150 dpi image]
[300 dpi image]
Fancy Star
[PDF]
[Encapsulated PostScript]
[72 dpi image (shown)]
[150 dpi image]
[300 dpi image]
G4G5, prepared for the 5th Gathering for Martin Gardner
[PDF]
[Encapsulated PostScript]
[72 dpi image (shown)]
[150 dpi image]
[300 dpi image]
Jackolantern (make out of orange paper!)
[PDF]
[Encapsulated PostScript]
[72 dpi image (shown)]
[150 dpi image]
[300 dpi image]
Entire Tangram Set from a Square
[PDF]
[Encapsulated PostScript]
[72 dpi image (shown)]
[150 dpi image]
[300 dpi image]
Last updated July 19, 2007 by
Erik Demaine.