8/14/2019 How to Fold a Real Easy Dodecahedron

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How to fold a real easy dodecahedron:

1. Start out with 3 regular printer-sized sheets of paper

2.

Divide them into 12 1 !ths "y folding in half "oth ways# creasing# wetting the sides# andtearing

3.

$ow# fold all those sheets in half twice# "ut this time unfold and don%t lic& or tearit...unless you were 'ust thin&ing of ma&ing a tiny dodecahedron out of 12 of the 1(s)uares you%ll have out of one sheet. :*+

!.

$ow that you%ve folded , unfolded your rectangle so you can see the center - fold all

the corners to the center# opposite corners at once - the point is that we want to "e left

8/14/2019 How to Fold a Real Easy Dodecahedron

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8/14/2019 How to Fold a Real Easy Dodecahedron

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>he dodecahedron is made from 12 pentagons. >he pentagons can "e made as follows.>hey are not e act pentagons# "ut they are close enough to ma&e an origamidodecahedron.

Start with a s)uare of paper. >he first step is to fold the paper into thirds. ?ou can useyour favourite method. 6n this e ample# @a mathematicians method+ the two diagonals

folded in the first picture intersect at a third along# and a third up the paper.

Here%s another way to fold a sheet of paper into thirds# which 6 learnt from the origami-lmailing list.

?ou ta&e your paper you want to fold in thirds# and some lined paper:

?ou thin& a"out four e)ually spaced lines# 1#2#3#!# and put one corner of the paper youwant to fold on line 1# and one on line !:

>hen you fold so the corner c touches "# and fold along from a:

8/14/2019 How to Fold a Real Easy Dodecahedron

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>hen fold along from " to get paper divided nicely into thirds.

Anyway# suppose you%ve got your paper divided into three.

$e t# fold over triangles of sides 1 and 1 3# as "elow. >hen fold over the other cornersalong the lines made "y the first triangles folded over. >hen fold the whole thing in half.>he angle at the top is pretty close to 1BC degrees. 6t%s not e act# "ut this is 'ust a poor

man%s pentagon. @what you do get# is that since you folded a third of the paper# there%s anangle that%s arctan@3+# which is pretty close to 42# and the angle at the top is 1CB-arctan@3+.+ @ ell# there%s another pro"lem that the sides of this diamond shaped thingmight not "e )uite all e)ual "ut they are pretty close.+

>hen you have to fold over the long pointy parts to ma&e a pentagon shape. >here arecreases you can match the points up with that give reasona"le side lengths. @ie# the linesthat divided the paper into three they give lines from the points to a point on theopposite side to fold to.+

=inally# to ma&e things a "it more secure# open it out a little now you want to slip flapa underflap " you do this while "ringing the two points la"eled c together# andthis ma&es them stay together "etter.

8/14/2019 How to Fold a Real Easy Dodecahedron

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>hat%s the pentagon done now. All you have to do is ma&e 12# and fit them all together "y putting the pointy "its into the slots created along the upper two edges of the pentagon.

$ote that there is one edge that is niether a point nor a slot you%ll get 12 of these in the

total dodecahedron# and you should ma&e sure they match up in ( pairs.

$ote# if you use the ruled paper method# and only ma&e one of the third creases# andthen use the folded over edge of that one side of paper to mar& where to fold from# youwill end up with a pentagon with no creases on one side# and so you get a pretty neatdodecahedron.