Another Way to Build the Klein Bottle

An update on my progress with the Klein bottle:
The next two images below are of my second attempt at building a Klein bottle, using the same coiling technique and focussing on exploring a way to resolve the issue with the transition from inside to out/outside to in, as explained in the previous 'Klein Bottle' posts, dated 9 and 16 April. Here is an excerpt: "Like the Möbius, the Klein bottle is a continuous form. It has one continuous surface, so if you let your eye or finger travel along it, you will cover the inner surface and the outer surface in one continuous movement. With the sculptural form - as opposed to a computer-generated animation: time evolution of a Klein figure - you have to cheat a little and squeeze through the small gap I have made. I'm hoping that I will find a better sculptural solution in due course."

The 'small gap' of the first Klein bottle became a series of holes in the second. I felt that this would deal with the problem of allowing passage between inner and outer surface. The result was unsatisfactory, regardless of the fact it is a working maquette; it just doesn't work sculpturally. 

Time, therefore, for version III. This time using a different building process. 

Pure joy! Right from the start. Instead of coiling my way up an inert form as before, here I had an alive, a moving gesture right from the first coil (a much fatter and flattened one, but still a coil). And the glorious curves kept coming:

The starter coil

And continuing to build

The completed form - interestingly 'organic'

With a different solution for "the problem of allowing passage between inner and outer surface"

Sculpturally satisfying, with freedom/invitations to generate edges and texture through the working gesture and process 

I feel at this stage that the 'hole' solution is a good one, although it will require sensitivity to form - one of these two holes is better than the other, the top one (inside the loop) is better integrated than the one underneath the loop.

Meditation (Part II)

Inspired by what I had read the day before (see previous post), I decided, yesterday, to set aside the next three consecutive Shed sessions to focus on a process of making one Möbius maquette at each session; to concentrate the mind and explore what different sculptural forms will/can emerge. (This plan has come about because of a forthcoming [enforced] absence from my Shed and I feel there is insufficient continuous time to complete one larger piece satisfactorily.)
The first step in the process is to form the Möbius plane: I begin by making a sphere (essentially the archetype of all form) - of a size that fits comfortably into the palm of my hands - simply by applying gentle steady pressure with the full palm of both hands onto an uneven lump of clay - a wonderful meditative process - which then very gradually transforms into a beautifully restful sphere. I then start gently pressing with my thumb into the centre from the two opposing sides, steadily alternating sides, forming two concaves, until the two concaves meet and a hole appears in the centre. I'm now holding a - somewhat mundane - ring-doughnut shape, or a torus in topology-speak.
From there the clay mass is gradually squeezed, constantly turning, and pressed into a rotation that flips it top to bottom, thus forming a Möbius - a MAGNIFICENT moving plane, and what makes it magnificent is that it is one continuous plane, moving round and round.
The first has become a very simple band with a slight thickening of the clay mass responding to/balancing the opposing 'crucible', the intersecting of the concave and the convex, i.e. the saddle plane or double-bent plane:

The 'crucible', where the concave and the convex intersect

The 'crucible' on the reverse side

Meditation ...

Voilà que hier j'ai lu quelque chose de merveilleux: 
"Ayez le coeur pur comme le crystal, l'âme vaste comme l'univers, l'intellect lumineux comme le soleil et l'esprit puissant comme Dieu", ce dernier je l'entends comme 'le Cosmos'. ...

The Figure of 8 - double Möbius

A maquette playing with the figure of 8 with a double Möbius. Of course the double Möbius makes this figure of 8 a two-sided form again. I will need a triple to make it all one-sided again. Am working on that one ... I am continuing with the maquettes in order to expand my understanding of these non-orientable forms. 
In the meantime:

The Klein Bottle (Part II)

The Klein bottle maquette has now been fired. I was slightly hesitant at first to do what I had set out to do from the outset: cutting the form in half seemed so brutal, but that had been the intention all along, it was its raison d'être ultimately, so, helped by the fact that I find the outer form rather clumsy - and in theory is not a proper Klein bottle because it is 3-dimensional and lacks its 4th dimension, time (more about that later) - I found the process rather satisfying because it did what it was supposed to do. It gives me a view of the inner workings, which helps me better understand the Klein bottle form.  

Like the Möbius, the Klein bottle is a continuous form. It has one continuous surface, so if you let your eye or finger travel along it, you will cover the inner surface and the outer surface in one continuous movement. With the sculptural form - as opposed to a computer-generated animation: time evolution of a Klein figure - you have to cheat a little and squeeze through the small gap I have made. I'm hoping that I will find a better sculptural solution in due course.

This is one half of the 'cheating' little gap

And the Klein Bottle

The first step in the Klein bottle exploration - a maquette (unfired) cut in half lengthways to look at the inner workings and clarify the form in my mind, and to  find out what the technical challenges are in the making process:

This is one of the two crucial places - where outside becomes inside (or the inside becomes the outside if you're taking the movement/travel in the opposite direction)

And this is the other crucial place - where the inner cylinder folds over and out of itself, the inside thus becoming the outside (or the outside becoming the inside if you're going in the opposite direction) 

And a couple of close-ups of the inner workings - during the initial stages of construction: