This origami dragonfly is a traditional model. It does use cutting at one point so is not pure origami.
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Start with an origami bird base. Fold the rear flap downwards as shown.
Next fold the lower right flap up and out 90 degrees as shown in the next four (4) photos.
Repeat on the lower left flap.
Now take point A and fold it to the centerline. Squash fold the left flap flat, then repeat on the right side flap.
Next flip the piece over. Fold point B towards the centerline, and squash fold flat.
Repeat on the right side. Fold the dragonfly in half as shown.
Rotate the piece 90 degrees clockwise. Then do an outside reverse fold to form the head.
Do a couple of inside reverse folds, then an outside reverse fold to finish forming the head.
Use scissors to cut the wings in half lengthwise. Then inside reverse fold the tip of each of the four (4) wings.
Fold the wings down and out as shown. Now your origami dragonfly is complete!