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The first step includes ruling out 20 equilateral triangles of the same size. Each corner angle will be 60 degrees and each side is six inches long. Once measured and drawn, the triangles are cut as precisely as possible. This can be cut with a strong pair of scissors, a box knife with a cutting board, or just a very strong paper cutter.
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Once separated, the triangles need to be reassembled into their new shape. An icosahedron is merely one shape that can be assembled. With different numbers of triangles, more shapes may be achieved. Other building materials are usable as well. Balloons and chicken wire both make good supporting structures for paper mache, although not necessarily at the same time.
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Tape is first applied to the inside of this structure to aid in the 'hinging' of the triangles. Tape on the outside will probably work fine as well, but it may bunch oddly until the final shape is achieved. If you want to make object into a piñata, this is the time that the candy should be placed inside.
The wheat paste should be mixed with a minimum of water. Ideally, it should be the consistency of thick oatmeal. It can be mixed thinner, but the more water in the paste, the more likely the cardboard is to warp. The normal manner of application includes dipping scrap paper into the paste, rubbing the paste into the paper, gently removing any excess paste with fingers and wrapping the form in multiple layers. The entire form cannot normally be wrapped at once, since a dry portion must be left on which it can sit. I wrapped most of it and then allowed it to dry over night. When I returned the next day I turned it over and wrapped the last couple of triangles. Multiple layers can be applied to make the form stronger.
The scrap paper used here is actually institutional paper toweling. Any cheap and absorbent paper will work well including newspaper or copy paper. I used paper towels because they dry strong and are evenly colored with a nicely porous surface fit for holding paint.
Once dry, the form can be either covered with more layers of paper or painted. Decorations may also be applied if desired. I plan to make this shape into a 20 sided die, and I want it to have a marbled look. For this project, I have chosen 'Make it Marble!' Tuscany Black spray paint for a quick marbling effect. This sort of paint gets all over the place, and so I have used another panel from the same box as a drop cloth. Since it takes a while to dry, I let the base coat set over night before turning it over and spraying the bottom.
Putting numbers on the sides is easiest by using a stippling brush with acrylic paint and stencils. To increase durability, I sprayed the entire shape with a couple layers of clear spray paint to seal the numbers.
By using the same techniques, any desired shape can be built and finished. Here are just a few.
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