Hexagonal Cross-Section of a Cube

It is a fun and challenging exercise to imagine all the different types of polygons that you can make by cutting a piece off of a cube with one straight cut. (In mathematical terms, the intersection of a plane and a cube.) For example, if you cut one corner off the cube, the surface that you expose is a triangle. Can you make an equilateral triangle, isosceles triangle, scalene triangle, trapezoid, or pentagon? This model shows that you can create a regular hexagon.

Steps

1. See general instructions for making polyhedra from nets.
   

Notes

• If you place eight of these sections of a cube back-to-back you can create a truncated octahedron.
  

References

• (Loeb 1991)