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Paper Play

Geometry & modular

Regular hexagon

Find 60° in a square, fold an equilateral triangle, then fold its three corners to the centre: a regular hexagon.

  • DifficultyIntermediate
  • PaperSquare, 15 × 15 cm
  • Steps8
  • About6 min

Why this level: Each fold is simple, but the corners must meet the centre point exactly for a neat hexagon.

You need: 1 sheet of origami paper

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Story

People have folded hexagons for a long time: the Public Paperfolding History Project has collected many ways to make one from books of the 1800s, kindergarten books among them, and some start from an equilateral triangle. T. Sundara Row’s 1893 book gives the simplest: fold the three corners of an equilateral triangle to its centre, and you get a regular hexagon whose side is one third of the triangle’s side.

Did you know? The triangle can be cut into nine small triangles. Fold in the three corners and the hexagon that is left is six of them — exactly 2/3 of the triangle’s area.

Learn more (external sources)

Steps at a glance

  1. 1. Crease the centre line

    White side up. Fold in half side to side and unfold to make a vertical centre line.

  2. 2. Bottom corners to the centre line

    Fold the bottom-right corner onto the centre line, creasing from the bottom-left corner. Pinch a mark where the corner touches, then unfold. Do the same with the bottom-left corner.

  3. 3. Fold the top strip down

    Fold the top strip down toward you along a horizontal line through the mark.

  4. 4. Fold the left side

    Fold the left part over along the line from the bottom-left corner to the top point.

  5. 5. Fold the right side

    Fold the right part over along the line from the bottom-right corner to the top point. You have an equilateral triangle.

  6. 6. Bottom corners to the centre

    Fold each bottom corner up to the centre point where the creases cross.

  7. 7. Top corner to the centre

    Fold the top corner down to the centre point too. All three tips meet at one point.

  8. 8. Turn over: done

    Turn it over: a regular hexagon with six equal sides.

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