Don't be discouraged by the seemingly complexity of this model or the amount of creases necessary. it is actually fairly easy, and with practiced hands can take less than three minutes to make. Enjoy, and please vote for this of you like it!
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Step 1: Material
You will need one sheet of square origami paper.
Avoid contruction paper or any paper with similar consistancies; they do not end up in clean finished prouducts. Computer paper works fine if you cannot find anything else. (Actually, normal comuter/ printer paper is ideal for most origami projects, its just not colorful. It gives nIce clean folds and is fairly cheap as well as easily accessible.)
Step 2: Creasing
There are many creases in this model, but they are relativity easy. try to make nice even creases now, it will save you trouble later.
Basically you need to make a 6x6 square using creases. There are two ways to do this. You can either fold the paper in thirds, and then each one of those thirds in half, or you could fold the whole paper into an 8x8 square and cut of two rows or squares from two of the sides (No picture). If you are a beginner, I highly recommend you try the second method, folding thirds can be a pain with unpracticed hands.
Like the famous saying goes, a picture is worth a thousand words. Refer to the pictures for a better understanding
Step 3: Creasing Continued
Take the bottom of one side of the paper and fold it up to the top one sixth crease. Repeat on all four sides.
Then take the bottom edge of the paper and fold it up to the closest one sixth crease.
Once again, refer to the pictures.
Step 4: Mountain Folding
The pictures should explain the next four folds better than I can. Its basically using the creases you created before to guide you in making the following mountain folds.
Step 5: Squash Fold
Once again words do not do justice. Please refer to the pictures.
But if you don't completely understand, you basically create the triangles by grabbing the corners and fold them to the center line. You then unfold, grab only the top layer of the paper, and fold it up to the upper crease. You then flatten it. You should end up with a dimond shaped fold. Repeat on all four sides.
Step 6: Flip, Fold, and Tuck
Name says it all. Flip the paper, take two opposite sides and fold to the center. Take the remaining sides and repeat, this time tucking the ends under the raised folds. Flatten out the model.
Step 7: Finishing
Pictures explain these folds. Basically fold out to create a crease, then tuck the corners into the model
Step 8: Poof! Its There!
You're almost there! But this last step is strange. Its similar to the origami water balloon/box in the way where you have to inflate it. You need to tug on the sides of the raised platforms until the general shape begins to form. Then smoothen out the sides. Then congrats! You're done.
Enjoy your vase. :)