Cube to regular Hexagon

• How would you cut a plane through a cube, such that its intersection with the cube would be a regular hexagon?
  
  
  Read my next post for the Right Answer of this Question:
  
  
  
  
• Right Answer of the last asked Question is here:
  
  Tom and Britney were two long distance lovers. Tom lived in Chicago, and Britney lived in New York. Tom was eager to get married soon. Britney, who wanted to concentrate on her career, wanted to delay for at least two years. Knowing that Chicago and New York have a time difference on an hour, Britney told Tom over the phone that if he proposed at a time when both Chicago and New York have the same time, she would(may) agree to get married right away. Within a month, Tom proposed, and Britney agreed. And the married couple, at least for Tom, lived happily ever after. How did this happen? When did Tom propose?
  
  
  
  

  Tom proposed on the last Sunday of October. At 2 AM, in New York, the clock was set back one hour into the Standard Eastern Time. At Chicago, it was still Daylight Time, which ends an hour later. During this hour, both New York and Chicago has the same time.