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Turn Four Cubes into a Truncated Octahedron

If you cut a cube just right, you will reveal a hexagonal cross-section. If you rearrange the pieces from four such dissections, you can assemble a truncated octahedron.

Materials

• Re-stickable (not permanent) glue stick
  
• Card stock
  

Steps

1. Build four copies (eight pieces) of the project Hexagonal Cross-section of a Cube.
   
2. Apply re-stickable glue stick (if you have some handy) to the surfaces to help the model stick together in a non-permanent way.
   
3. Assemble the pieces so that all the vertices that used to be corners of the square meet in the middle of the truncated octahedron.
   

Notes

• While any polygon can be dissected into pieces that can be rearranged into any other polygon with a finite number of cuts, the same is not true with polyhedra. For example, it is impossible to dissect a tetrahedron into a cube using a finite number of cuts.
  

References

• (Kappraff 1990, 332-3)

Comments

  © Laszlo Bardos