"Urs Holzer" <urs### [at] andonyarcom> wrote in message
news:488a193c@news.povray.org...
> Warp wrote:
> > B. Gimeno wrote:

> >> ....also known as Klein's Surface, this is a test of the almost
> >> finished new version of the bastard tiling shapes from hell include
> >> file.

> >   Personally I have always had a problem accepting klein's bottle as a
> > true *borderless* surface because the surface intersects with itself,
> > and the intersection could be interpreted as a border.

Yes, it's a little disingenuous to call it a surface in 3D.

> It only intersects itself in 3D because it can not be embedded in 3D.
> But it can be embedded in 4 dimensions where it shows up as a true
> borderless surface.

Of course in 4D (which is inherently more interesting than 3D), it becomes
just a regular surface/volume, not much more interesting than the Moebius
band or even a torus in 3D.

Post a reply to this message