Fold the fox one step at a time and pause whenever you like. Ask me about any fold: why the ears match, what an angle bisector is, or why the nose is one third of the way up.

Paper Fox Face

A cute fox from one square — and the triangles and symmetry inside it

Fold a square corner to corner. The diagonal cuts it into two identical triangles, each with one 90° corner and two 45° corners. Two of its sides are equal, so it is an isosceles triangle. The long edge is the diagonal of the square, about 1.4 times as long as a side.

Fold the triangle in half and open it again. This crease runs from the square corner to the middle of the long edge. It is the fox's line of symmetry: it splits the 90° corner into two 45° angles, and the left and right halves of the face will be mirror images of each other.

Fold each side corner up and over, so the folded edge points to the middle of the slanted side. The edge has turned by 45°, so the crease cuts that turn exactly in half: it is an angle bisector. Do it on both sides and you get two matching ears. Finally, fold the top point down and behind along a line one third of the way up. That crease is parallel to the long edge, and the point sticks out below as the nose. The nose is still a 90° point, because it is made from the same two 45° sides.

Notice that the finished face is exactly as wide as the side of the square you started with. Pause on any step and ask the tutor why the ears match, where the angle bisector is, or why one third makes such a good nose.

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How do you fold an easy paper fox face?
Fold a square in half corner to corner to make a triangle, with the square corner pointing up. Fold the right and left corners up and over to make the ears, then fold the top point down and behind to make the nose. It takes about six steps and works well for children from about 6 years old.
What paper is best for an origami fox?
Any square sheet works. Thin, crisp paper creases best, and an orange or red sheet makes a lovely fox. Ordinary printer paper cut into a square is fine. A square of about 15 cm (6 inches) gives a face that is easy to hold.
Which math is hidden in the fox face?
Right isosceles triangles (45°, 45° and 90°), a line of symmetry, angle bisectors, parallel lines and thirds. The long edge is about 1.4 times a side of the square, which comes from the Pythagorean theorem.
Why do the two ears look the same?
The paper is symmetric about the middle crease, and the second ear is made with the same fold on the mirror side. Mirror images always have equal angles and equal lengths.