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Lesson 6 of 20 · 9 moves

The Hexagon

Inscribe a regular hexagon in the circle, starting at P.

OP
The finished construction: the figure in gold over the lines that found it.

The radius of a circle steps around its rim exactly six times. No other polygon fits its own radius so perfectly, which is why bees, basalt and snowflakes all choose six.

Walk the compass around the rim, then join the steps.

Try it in Construct

The app snaps to every crossing, checks your construction exactly, and offers hints one move at a time.

Step by step

  1. OP

    Circle centred on P through O: it marks two corners.

  2. OP

    The line through P and O finds the opposite corner.

  3. OP

    Circle on the opposite corner through O: the last two corners.

  4. OP

    Join the corners: all 6 sides.

What it shows

Six equilateral triangles meet at the centre: the hexagon is the vesica repeated around a circle.

The figure