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Lesson 20 of 20 · 15 moves

Metatron’s Cube

Find the cube and the star tetrahedron hidden in the Fruit of Life.

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

Join the thirteen centres of the Fruit of Life with straight lines and all five Platonic solids appear as shadows. Here you will draw two of them.

The outer hexagon with three spokes from the centre is a cube seen corner-on. The two great triangles are the star tetrahedron.

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. Join the outer centres into a hexagon.

  2. Continue the hexagon (5 times).

  3. Three spokes from the centre to alternate corners make a cube.

  4. The second spoke.

  5. The third spoke: a cube, seen corner-on.

  6. Now join every second outer centre: two great triangles.

  7. Continue the triangles (5 times).

What it shows

A cube and a star tetrahedron, flattened into the plane. Lift the figure in Explore to see them stand up in space.

The figure