From another dimension

It has arrived from another dimension!

Just follow the trail: http://www.youtube.com/watch?v=a8sWLDGxDF4 ----> http://shpws.me/3lIs

Excellent! It is a Klein bottle, right? But with an axis of symmetry...
Well done!
Like the video too...

Very cool... could you do something similar with this model of the Klein bottle?

http://www.geom.uiuc.edu/zoo/toptype/klein/figure8/

Thanks!
Means a lot coming from you both

It is sort of a double Klein bottle I think, but Klein is normally non-orientable, while this one is, although inside and outside get swapped here and there

I have been working on a Klein eight https://www.shapeways.com/model/337239/ but was not yet sure how to continue in making it printable/visible.

Very cool model Virtox

And the figure 8 klein looks good too.

Paul

Thanks!

As HenrySeg also suggested, I am looking for ways to merge the two forms.
It will probably be a while before I can bend the Klein Eight to the shape I am looking for.
Took me a bit over two years and 50+ (complex) variations to get from the basic 8-torus to the Pharamo

And the Klein Eight is a very inspiring and fascinating shape with a lot of potential.
More so than the original Klein, which I have always found fascinating, but somehow not very esthetically pleasing.
Although Bathsheba did an excellent job.

I love discussing the Klein (Eight) further, but to keep it a bit more on topic here, I added an open WIP thread for math shapes:
https://www.shapeways.com/forum/index.php?t=msg&goto=3566 6

I hadn't realised that it was actually orientable

Did you try a symmetrical version, so that if you turn it upside down it's the same?

Haha, well to be honest, for a long time while I was working on this I thought it was non-orientable. Until I started working on a textured one I realized it actually was

At first I started with a basic symmetric versions:
https://www.shapeways.com/model/50742/
https://www.shapeways.com/model/320015/

And tried many times to find a pleasing surface, sometimes symmetric, sometimes not.
But when I finally had the asymmetric Pharamo version, I had to make a symmetric one too:
https://www.shapeways.com/model/320880/

Edit: typos

Very cool... I think you're right in highlighting the non-symmetric version, it is a more interesting object.

Ok here's an idea: there should be a way to smoothly deform between the two styles of holes/strands. How about moving back and forth between these two styles as we rotate around the object?

Virtox, you talking about Fig. 11 a ( https://www.cs.berkeley.edu/~sequin/PAPERS/2011_Bridges_ToriS tori.pdf)?

I suppose the next progression from that would be multiple double klein bottles arranged in a ring with the top and bottom bottles offset by one around the circle.

Maths formula isn't a strong point for me, I've a touch of dyslexia that gives me brainache looking at equations, but imagining how a structure is built and figuring how to make it work I can do

The works of Charles O. Perry are quite inspirational too... I managed to replicate his Indiana Arc. My model is here

@Henry, yes that should make for a very interesting variation

@Paul, yes 11a was what I meant indeed, I am trying to imagine a tetrahedral-like variation, where each "point" is the bottom of a Klein bottle of sorts.
Where each would have three other "bottoms" to connect to.
As far as I can tell, the surface should also be orientable then.

Very cool design.

Hurts my head to think about it, so I just look at it and all is well again.

Lincoln

Thank you

Added some better photos, still not 100% satisfied though, the WSF polished is even very difficult to photograph,
so I got myself several sheets of large cardboard in different shades white to black, this is medium grey:


Pharamo

Wow the pictures look like rendering (this is a compliment ).
Very beautiful model, definitely.