crafts,  homeschooling

Origami Stars

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Origami star made out of a regular hexagonal piece of paper. Any paper is fine, you don't need special origami paper.

It’s almost time to start making some homemade Christmas Tree Ornaments, and last night I finally figured out how to make an origami star.

one way to fold regular hexagon uses a triangular piece of paper

You need to start with a hexagonal piece of paper. There are two easy ways to make a hexagonal piece of paper and I’d like to share both of them with you. The first way if to fold a square in half, so it is a triangle, and then to fold the two tips up across each other at about about a thirty degree angle. Think of it as a triangle giving itself a hug. Now you have six layers of paper all folded together and all you need to do is trim the top off in a straight line and unfold.


The second way comes from the RightStart Mathematics Program, Level D (except the author of that program explains it much better than I do). You take a rectangular piece of paper and fold it into quarters the long way. Then unfold it so it is in halves, folded part on the top, with an extra crease across the middle. Take the corner and touch it to the crease across the middle.

hexagonstep2Cut off the folded part so that your paper looks like this. You can clearly see sides of what will eventually be your  love this step in making the regular hexagon, because suddenly what was the side of the hexagon looks parallel to the top and part of what was the bottom helps you measure the side. All the edges transform in some way.hexagon. You are trying to make a regular hexagon, so all the sides have to be the same length, so you’re going to use one of the sides you already have cut to measure the distance the next side needs to be.

Fold the paper diagonally so that the top “finished side” is against the top of your paper. Use the edges already done to show you where to cut and remove the extra paper.

Now, to make your hexagon into a star you need to fold and give yourself lots of crease lines. You need lines connecting every second corner. You can start with each corner and fold it down then move to the next corner or you can do opposite corners thus making a rectangle each time. The picture to the left shows four of these lines. With two more fold lines the creases would look like a beautiful star, though not the same size as the star that will eventually be folded.

Once you have crease lines connecting each corner to the second corner over from it, the next crease lines to put in are ones dividing the flat edges in half. Just fold the hexagon in half, unfold, rotate and repeat.

You want all the crease lines shown in my the two-colored picture. If you think of the middle part as a star you need to fold the tips of the star towards the center as though you were making a hexagon again. The part that I have colored green is going to form little extra flaps like the six legs of a hexagonal coffee-table. Fold them so that they form pairs pointing towards each other and lie flat.hexagonpentagon
Now your shape should look like a regular hexagon made out of three irregular pentagons. Take the inside tip of each pentagon and fold it outward so that it touches the outside of the hexagon. Take a moment to admire the beautiful pattern created
hexagonsopenedNow the next part is to take the little triangular points that stick into the center of your shape and fold them upwards. At the same time you fold everything that is above them down back. I drew the fold lines I’m talking about making in red. If like me you personify everything then you can think of the triangle as being the head of the star and by folding back everything above it you create the star’s shoulders. Rotate the shape and repeat again until you have a full star shape.

shouldersOn one side the star should be nice and clean with six triangles attached to a hexagon. On the other side it probably looks like a mess of papers.  By inserting the papers inside one another you should be able to make that side look nice too.

If you are obsessive about math you can figure out the relationship between the original hexagon and the final star.

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