Re: D=5

["John S. Denker" <jsd@MONMOUTH.COM>]

Robert Cohen wrote:
> > >             _______
> > >           /|      /|
> > >          ________/ |
> > >         |  |    |  |
> > >         |  |____|_ |
> > >         | /     | /
> > >         |_______|/
>
> If I never experienced a 3-dimensional object, I would see the drawing above
> as two 2-D squares with their corners connected.

Please look again.

1) You should be able to see that there are _three
different ways_ in which it can be decomposed into
squares with their corners connected.

2) You can also imagine how the various squares slide
relative to each other when the viewpoint of the
projection is changed.

3) You can arbitrarily label various pairs of squares as
the XY, YZ, and ZX faces.

=========

The same goes for hypercubes.
  http://www.monmouth.com/~jsd/physics/gif48/tesseract.gif

1) There are four different ways the hypercube can be
decomposed into pairs of cubes.
   http://www.monmouth.com/~jsd/physics/gif48/tesseract-chop.gif

2) You can imagine how the cubes slide relative to each
other when the viewpoint of the projection is changed.

3) You can arbitrarily label certain pairs of cubes as the
XYZ, YZT, ZTX, and TXY hyperfaces.


===============

I think it's amusing.  My neices thought it was amusing.

If you expect it to be clear at first glance, you're
expecting too much.  You have to stare at it for a good
long while.