P3D n-dimensional projections

[Nick Merz <merz@xxxxxxxxx>]

>
>Bruce Springsteen (p3d 3769):
> >By definition, a depth-impossible object cannot be presented
> >in stereo, and the examples I've seen, by A. Girling and Udo
> >S. and Holten, only demonstrate that fact.
>
>Indeed, an impossible object is impossible in stereo,
>but I not only like impossibilities but also paradoxes :-).

This dialogue reminded me of a question I've meant to ask.
Has anyone on the list seen (or created) 3D projections of higher 
dimensional geometries?

I have occasionally seen 2D representations of these (often just 
computer screen shots printed in magazines), but never known of 3D 
versions.  I would be particularly interested in 4D objects projected 
into 3 space.  For example, I know it's possible to tie a plane into 
a knot in 4D space without having it pierce itself, but I've never 
seen it in 3D.  I have also seen 2D attempts at a hyper-cube, but 
never a 3D.  I can imagine a cool Viewmaster set where you project a 
Hypercube into 3-space, than rotate it incrementally around one axis. 
One reel is seven views around X, one is Y, and one is Z.  360/7 is 
your angle increment.

I would be surprised if no one has seen or made some of these, given 
the brain power on this list ;-)

ciao,
nick