Triangle
In origami it is natural that the triangle is equilateral, just as the natural base is a square, where the sides are the same length. Triangles are the first planar object that can be made with the fewest number of line segments (two line segments just are not up to the task).
There is an easy way to make a lot of equilateral triangles, starting with a strip of paper of uniform width. Even if the first fold is only approximate, the following folds can be made "perfect" as long as the corner is tight and the edge aligns with the existing edge.
Making an equilateral triangle (or equivalently, 60 degree and 30 degree angles) is as easy as making two folds on a rectangular piece of paper. Say we start with a letter size piece of paper, long side up and down (sometimes this is called "portrait mode") and fold it left to right in half: the resulting fold is vertical. If you take say the upper left corner and put it on the centerline, while adjusting its location so the crease ends up including the upper right corner, and set the crease, you have a 30 degree angle from the top. Folding the paper over where the top edge has landed, makes a 60 degree angle. Using the point on the centerline as a reference point, complete the equilateral triangle. Voila! Constructing 30 and 60 degree angles with two folds can be done almost anywhere with a bit of planning, and it's good to know this shortcut to make an exact 30 or 60 degree angle.
Strips of paper folded into connected equilateral triangles in this manner are very nearly ready to make a basic hexaflexagon. https://en.wikipedia.org/wiki/Flexagon shows how to make a hexahexaflexagon.
I've used a hexaflexagon to write brief messages that are hard to decipher until the flexagon is returned to its state where the message was originally written.
See also:
Triangle unit origami
Flexagon, Hexaflexagon, Hexahexaflexagon
