Folding a 24-card cuboctahedron

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Folding a 24-card cuboctahedron
Rachel Grey, lemming_at_alum.mit.edu
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Step 1
Get 24 business cards together (plus extras in
case of mistakes). Hold one with the printed side
toward you, right side up.
Your card now looks like this.
Now fold down the upper corner. The existing
shape of the card will guide you (your new fold
lies along the edge of the card that doesnt show
in the picture).
Fold the lower left corner to the upper right
cornerpinch corners together, then squish with
fingers to make the crease.
Your card has one mountain fold and one valley
fold. Let go and let each fold relax to about a
90 degree angle, but dont flatten the card
again. Repeat these folds for all 24 cards.
(Look! An equilateral triangle!)
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Step 2
Hold a card in your left hand, gripping it by its
equilateral triangle. Now take another card and
put the part shown in red on the 2nd card over
the part labeled in red on the first card. Fold
the small triangular flap over the first
card. Pinch to keep the cards together. Transfer
this pinch to your left hand. Then put a third
card over your second card in the same way and
pinch again. Hold all this however you can and
add a fourth card, which wraps over the 3rd card
and is itself wrapped over by the first card (got
it?).
The unit you get looks like this from the top.
The triangular flaps are all folded down a bit to
keep the unit togetherotherwise the view from
above would be a perfect square. Underneath, the
parts of the cards you cant see are making a
spiral shape that lets the unit sit flat on the
table. Use your 24 folded cards to make 6 of
these units.
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Step 3 just do it
Study the picturesee how three of the units from
Step 2 are clearly visible, and the triangular
flaps weave together to make the 8 outer
triangles of the cuboctahedron shape? This shape
is not as complicated as it looks--its just a
cube with all 8 corners cut off. Your six units
will all be at right angles to one another as if
they were the six faces of that cube. When
joining two units, the picture below left shows
the two line segments that have to come together
and where you can begin tucking flaps under one
another. Ive shown the units from above,
although the joining is easier with both units
upside-down. (Note As you look at the units
undersides, there is a stronger way and a weaker
way to put the units together, depending on
whether you simply let them rest next to each
other or push the cards into slots formed by the
units structure. The stronger way will give you
a stronger final product, but you probably wont
be able to do it for all unit-to-unit
connections.)
As you go along, keep cupping the structure in
one hand while adding new units with the other.
Interweave the small triangular flaps at every
opportunity to keep it strong. You will have to
disassemble the sixth unit and put the cards in
individually, and putting in the final card will
require loosening of a large part of the
structure.
tuck under
tuck under