slicing cubes with planes
sometimes itās good to think about elementary problems. One reason is because thinking about elementary problems lets you appreciate abstraction better! Elementary school fact: you can slice a cube with a plane to produce a hexagon. In order to do so, you will need to intersect all 6 planes of the cube. (In fact, any plane which intersects all 6 sides of the cube should get a hexagon.)
For example, hereās one slice (from Wikimedia commons)
Why it works: A hexagon has 6 sides; these correspond to 6 lines. The intersection of two non-parallel planes is a line. Thus a plane which intersects all 6 sides (bounded planes) of a cube will make a hexagon.
















