07-24-2010, 01:33 PM
I can help with that one.
A 3D cube as represented in a 2D flat picture:
![[Image: rubiks-cube.jpg]](http://www.mathfail.com/rubiks-cube.jpg)
A simplified picture of a 3D cube, using a single line to represent each edge of the cube, but with hidden lines removed (not being able to see through solid faces):
![[Image: plain_cube.gif]](http://deimel.org/images/plain_cube.gif)
Just the outline of a cube, edges only, as if you connected a bunch of sticks to make a wireframe outline:
![[Image: cube.jpg]](http://pballew.net/cube.jpg)
And without any contrast between the edges closer to us and those farther away:
![[Image: image004.png]](http://www.edge.org/3rd_culture/thaler_sendhil08/images/image004.png)
Trace around the outside of that image: six sides, but with a variety of lengths and angles.
Notice that if we look at the cube directly on one of its corners, the perimeter outline is a hexagon:
![[Image: Isometric-Cube120.png]](http://www.blendenzo.com/Images/Tuts/Isometric-Cube120.png)
A hexagon by itself:
![[Image: hexagon_36136_md.gif]](http://etc.usf.edu/clipart/36100/36136/hexagon_36136_md.gif)
So when we see a hexagon in a flat image, we have to ask, is it supposed to represent a flat hexagon, or the outline of a cube as seen from one corner of the cube?
A 3D cube as represented in a 2D flat picture:
A simplified picture of a 3D cube, using a single line to represent each edge of the cube, but with hidden lines removed (not being able to see through solid faces):
Just the outline of a cube, edges only, as if you connected a bunch of sticks to make a wireframe outline:
And without any contrast between the edges closer to us and those farther away:
Trace around the outside of that image: six sides, but with a variety of lengths and angles.
Notice that if we look at the cube directly on one of its corners, the perimeter outline is a hexagon:
A hexagon by itself:
So when we see a hexagon in a flat image, we have to ask, is it supposed to represent a flat hexagon, or the outline of a cube as seen from one corner of the cube?