why platonic solids?
my inspiration for this project was the print "stars" by amazing artist m c escher, or more exactly the "study for stars". I've added an image of the study for stars, this is not a picture i took myself! in this picture you can see the five platonic solids, along with 4 more complicated structures (that are made from combining some of the solids), as well as one rhomboid structure that i also made. this structure is more complicated, since there is some calculating involved. i will not include this shape in the instructable.

Step 1: You Need

- a rest of cardboard
- big sheets of thick paper ( i used A2), at least 120 g paper - i don't know how paper is measured in the non-metric world, but to give you an idea of how thick the paper should be: regular printing paper is 80 g
- ruler, a triangle, a pencil, small scissors, an exacto knife and a cutting mat
- glue, i used normal wood-glue to glue the paper and an all-purpose crafts-glue for the foil

- thin plastic foil in cyan, yellow and magenta:
do you know the crappy instant photo print machines that are found in shops like drugstores since some years? you can print photos from your usb stick or so and the quality of the photos is quite bad, but it only takes a minute for them to be printed. well these machines print their pictures using some kind of thin color coated plastic foil that has recurring sections of cyan, magenta and yellow. once a roll of this plastic is finished, they throw it away. which is a pity, since it makes for an awesome craftting material - for a example for a project like this. and since it is basically garbage, it's free! so next time you are in a shop with a photo machine like this ask the employees if they happen to have changed the roll just that day or if they can save you one the next time they'll change it.
the colors are stunning and you can still see "ghosts" of the once printed pictures.
if you cannot get your hands on a material like this look for some other transparent, colored plastic foil that is glueable to paper.

Step 2: Make a Cardboard Template

to make an icosahedron you will need 20 equilateral triangles. so let's make a cardboard template:
i chose an edge lenght of 16 cm. you could also make it smaller or bigger, as you like.
draw an equilateral triangle (all the angles are 60 degrees) of your desired size on a piece of cardboard, then draw another triangle inside the big triangle with all the sides being 1,5 cm apart from the big trianles sides.

with the help of a ruler and an exacto knife, cut out the big triangle and the small inside triangle, discard the inner triangle, you won't need it.

with this template you can also make a tetrahedron and an octahedron.

if you want to make the cube or the dodecahedron, you have to make a square or a pentagon template the same way.

Step 3: Drawing

now you need to draw the net of the icosahedron (or one of the other shapes) onto the paper with the help of the template. the paper i used was not big enough to draw the complete net on one sheet. if you are not using really big sheets of paper, this will happen to you, too.
start with a basic version of the net.
so you can find one version of the net on the wikipedia page of each of the solids, i used a slightly different version as a basis (first picture of my drawing) then i adjusted it so that i could fit as many triangles on one sheet as possible (less glueing later). to make what i did clearer, i numbered the triangles. the blue part on the second picture is the part i cut out of one sheet, the orange part i cut out of the second sheet. the red "20" triangle i had to cut out separately.
(with a smaller shape like the tetrahedron, all will fit on one sheet, see step 6)
after drawing all the triangles, you have to add glue flaps on one side of every egde where you later have to glue the different parts together. see third picture.

Step 4: Cutting, Scoring & Folding

once you drew all the triangles cut them out (including the glue flaps). an exacto knife is the best tool. don't cut the single triangles apart!
when you are done, you have to score all the lines that will later be folds: all the lines where triangles are connected to each other and all the lines where a triangle is connected to a glue flap. either you have some special paper scoring tool or just do it with the tip of the blade of some small and pointy scissors (and a ruler), see pictures.
after scoring, fold all the folds.

Step 5: Glueing

cut triangles out of the colored plastic foil, slightly smaller than the triangle template (in my case with a side lenght of about 15 cm).
glue the plastic foil triangles to the paper from the left side. see to it that no adjacent triangles have the same color, because that will look nicer on the finished solid. once you glued a foil behind every triangle window, first glue the seperate parts together (take a look at your plan from step 3 for help), then glue the whole solid together, one flap at a time. the last glueing will be a bit difficult because you can't press at the flap from the inside, but carefull work will get you there.
and your solid is finished!

Step 6: All the Steps for the Tetrahedron

here is the whole process again for a tetrahedron, since it is smaller, some details will be more clear.

Step 7: Hanging

if you want to hang your platonian solids from the ceeling like i did, attach a white or nylon thread (that way it will be almost invisible) to one corner of your solid with a needle. make a knot. since the shape weighs so little, you can just glue the other end of the string to the ceeling with some clear tape. as the light shines through, you can see how cyan and magenta make violet, magenta and yellow make orange and cyan and yellow make green.
have fun with your shapes!