A plane which passes through three edges of a cube produces a triangular cross section as shown. In two or more complete sentences, explain how the plane should pass through the cube in order to produce a cross section that is a regular hexagon. https://media.glynlyon.com/g_geo_ccss_2013/8/img_geo_8_20a_01_13.gif

Question

anonymous · Answer

@e.mccormick

e.mccormick · Answer

First, do you know what a regular hexagon is?

anonymous · Answer

A figure with 6 equal sides and angles.

e.mccormick · Answer

Yes.  So, it needs to slice somehow that it gets 6 sides.

anonymous · Answer

In the image, the triangle, or cross section, is what we are using to slice it right?

e.mccormick · Answer

You use a plane.

anonymous · Answer

So the plane isn't in any particular shape?

e.mccormick · Answer

It is an infinite flat space.

anonymous · Answer

So what I'm trying to figure out is where to place the plane to create a hexagon?

e.mccormick · Answer

Yes.  Now, as a hexagon has 6 sides, that means hitting everything.

e.mccormick · Answer

cube = 6 faces.

anonymous · Answer

Okay, so would it make sense is I said to use a square plane large enough to touch all inside faces of the cube?

e.mccormick · Answer

Well, a plane is infinite.

anonymous · Answer

So what would I say?

e.mccormick · Answer

Well, first off, have you ever looked at a cube from one corner?  I mean, look directly at the corner as the center of the view?

anonymous · Answer

What does that have to do with it?

e.mccormick · Answer

Well, what does it look like?

anonymous · Answer

Okay so what now?

e.mccormick · Answer

Well, what do you think would happen if you came at a corner like that, from the top down?  If you have a cube, a box or a die, it might help you visualize it.

anonymous · Answer

Okay I can visualize it, but what do you mean what would happen?

e.mccormick · Answer

Well, watch: http://youtu.be/F0YnyTkL45Y

anonymous · Answer

Okay I understand so far

e.mccormick · Answer

Well, did you see the regular hexagon you need?