The Maekawa Theorem

The Maekawa Theorem, which was named after Jun Maekawa, states that at every vertex in flat-folded origami, the difference between the number of mountain and valley creases is always two.
It is this difference between mountains and valleys that allows origami pieces to be flattened! This principle can be visualized in any flat-folded origami work by unfolding the piece, and coloring alternating sections around a single vertex.

A simple fold visually demonstrates the Maekawa Theorem. Notice how the orange and white sections of the unfolded paper alternate.

Grab a couple colored pencils and explore the Maekawa Theorem for yourself through a simple tutorial here, explore flat-folding with the classic paper crane, or challenge yourself and try your hand at the Miura-Ori fold!