Foldable maps (in construction)
Fold your own globe-in-a-box
Two of my passions and an old interest share this page:
- studying why and how flat maps distort features of a
spherical surface
- origami, Japanese word for the now international
art of folding recognizable or abstract figures in plain
paper
- creating a pseudoglobe in the shape of a polyhedron
Fujimoto's Cube
Perhaps the most elegant origami cube, the model created by the
great folder and researcher Shuji Fujimoto requires a single
square sheet of paper. You can print and fold a sheet creating a nice cubical world "globe". Cut the
big square and follow the small crease pattern included (it is
inside the square but will not appear in the final model) showing
valley and mountain folds.
Experienced folders should have no
difficulty folding the cube using the crease pattern alone, but
detailed diagrams can be found in at least two books (I doubt I
can draw better ones), [KT87]
and [Ja90], pages 38-39. Thoki
Yenn includes diagrams at his site, in the context of
the famous Delian problem.
As soon as I get the time, I plan drawing a map pattern for Kazuo
Haga's octahedron, also diagrammed in Origami for the
Connoisseur.
Montroll's Cube
More recently, John Montroll devised several origami polyhedra
folded from a single sheet.
His cube ([Mon02], pages 14-15)
is particularly elegant: all faces
comprise a single uncreased piece. Warning: this is a larger file
(560 KB); before printing, make sure it fits your paper.
Haga-Kasahara Cube
A cube superficially similar to Montroll's was previously invented
independently by Haga and Kunihiko Kasahara. It can be folded from
the same printed pattern for Montroll's, using diagrams in
[KT87], pages 58-59, mirrored
left-to-right.
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Crease patterns for Haga-Kasahara (left) and Montroll (right) cubes:
pale blue marks the external faces. Edge "A" should be on the top
at step 4 of [KT87] (all steps should be mirrored left-to right); edge
"B" should be on the top at step 5 of [Mon02].
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Miura-ori
Another interesting marriage of paperfolding and cartography
(or at least practical map usage) is presented by the
Miura-ori technique (named after its pioneer
Koryo Miura): folding a large sheet in a way which
allows instant opening by just pulling apart two corners.
Collapsing the map back is equally fast and easy. A similar
method ensures deployment of solar panels in spacecraft.
Almost identical diagrams for a Miura-ori sample
are included in
[ORU5], pages 34-37 and
[Kan97], pages 236-238.
 |  |  |  |  | | www.progonos.com/furuti June 25, 2003 |
