Thanks. I feel I should always point out that this is copied from a piece by Nat Friedman which is discussed in the discussion linked to in my original post!

It is nice to be able to pick up the item from the base and hold it.

Thanks. I feel I should always point out that this is copied from a piece by Nat Friedman which is discussed in the discussion linked to in my original post!

It is nice to be able to pick up the item from the base and hold it.

Very nice.

Here’s a piece I made myself recently. So far only as rendering and a small 3d print, but I would love to see it larger scale one day. It uses the Bryant-Kusner parametrization of Boy’s surface, but with a different projection than the usual closed one, and openings cut to avoid the self-intersections (and the arrangement of these openings was inspired by a hand drawn illustration in George Francis’ *A Topological Picturebook*).

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Also - that Charles Perry sculpture actually looks very close to something else I was looking at recently - related to a way of making a Sudanese Moebius band by sweeping a helix through a stereographically projected 4d rotation. Using a straight line instead of a helix gives you a zero thickness non orientable surface, but the nice thing about using a helix is that you can do the double cover and get a closed manifold solid in one go without having to offset.

The sweep creates a shape that goes to an infinite plane, and you can trim this to get a shape like the Charles Perry sculpture you linked, or you can perform another 4d rotation to close this up and get the Sudanese Moebius with a circular end/

SudaneseMoebiusSolid2.gh (14.1 KB)

SudaneseMoebiusSolid_Perry.gh (12.1 KB)

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I really like that! Very hard to make using subtractive manufacturing methods but I bet the 3d printed version is nice. What 3d print technology and materials did you use?

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that looks like an Oloid, at least the lower image reminds me of it. something which is actually very simple to produce in rhino, two circles lofted into each other. i was actually trying to find a way to introduce a third circle for the initial example in this topic, but that did not work out at all.

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An oloid is a quite different shape to the above. Try spinning this around:

SudaneseMoebius.3dm (337.5 KB)

Nothing fancy yet, just white nylon SLS

Yes, I imagine if trying to CNC mill a shape like this it would be rather challenging to get into those folds.

I guess pieces like the Michael Foster ones you linked above involve a lot of skilful and patient chisel work!

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Is there a split plane or surface that would divide it into 2 parts that could be machined from both sides on a 3 axis CNC? Is there a mathematical way of defining a splitting plane or surface? This can be quite an art when creating moulds but since the shape is so mathematical, can the split plane / surface be calculated so it splits the part so as to not leave any overhang on either side of either part?

I can’t open it to try