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.
- Re-stickable (not permanent) glue stick
- Card stock
- Build four copies (eight pieces) of the project Hexagonal Cross-section of a Cube.
- Apply re-stickable glue stick (if you have some handy) to the surfaces to help the model stick together in a non-permanent way.
- Assemble the pieces so that all the vertices that used to be corners of the square meet in the middle of the truncated octahedron.
- 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.