Streptohedrons

A couple of months ago David Springett came to the Hampshire woodturners monthly meeting and gave a demonstration. Amongst the things he demonstrated were what he called ‘streptohedrons’I wrote about them at the time, as I was inspired a great deal by his demonstration. They are cool because the shapes you achieve are interesting and complex, but the method is relatively simple to understand.

You take 2 pieces of wood of the same size, with nice flat square faces and glue them together with a piece of newspaper in between. This is a paper join. You then mount the piece between centres along the glue join, being careful that you don’t just split the piece along the join when mounting it.

Then turn a shape in this piece. The only important thing is that what ever shape you turn you need to control what the cross section through that paper join looks like. It must have rotational symmetry. In its most simple form you turn a cone. A cone has a triangular cross section, and turned correctly, that triangle can be made to be an equilateral triangle and hence have rotational symmetry.
The cool thing is that the principal applies to any shape you can think of that has rotational symmetry.

Having been inspired by the theory I decided to have a go. The first challenge is actually getting two blocks with flat surfaces that will produce a nice flat join. David said that for this you really want a planer-thicknesser that can just give you a smooth flat surface to work with. Unfortunately these are very expensive, and I don’t have one.

What I do have is a bench belt and disc sander. And the belt sander does a reasonable job of getting a flat smooth surface. Though it is pretty hard to actually get it flat over a large piece. However having done the best I could I set about gluing the two pieces together. Unfortunately I didn’t have any news paper, and resorted to using a piece from the back on an envelope. This was not a good idea.

Once it had dried I mounted it on the lathe and set to work turning a cone shape. Just as I was starting to form the shape it PINGED into two flying pieces. (Always wear your face mask!)
It seems that paper from the back of an envelope is too thick, and did not help form a strong enough join.

Fortunately every Thursday I get a free paper delivered which normally goes straight in the recycling. This time I saved some, and started again.

This time I turned the glued up block down to a cylinder, measured the diameter and set to work on the maths. Another thing I love about this (because I’m a geek) is that it requires some Pythagoras’ theorem. And this means I can hark back to the glory days of GCSE mathematics when I was actually good at it. Before the rude awakening that was A-level maths. Who needs to know areas under graphs anyway? You can’t use that in wood turning.

It would probably have been easier to figure out the nearest whole numbers that I could work with. But I figured I’d make the biggest thing I could in the diameter. All of this good maths just to figure out how tall to make the cone.
With that established and marked, all you have to do is turn a straight line between the bottom max diameter and the top at which you should reach a point.

I discovered at this point that I had not been sufficiently careful about lining up my centre points on the glue join, and the tip of my cone was slightly into one side and not the other.

However the magic of sanding allowed this to turn into an acceptable streptohedron anyway

They make quite cool things for just fiddling with. I have this on my desk at work. Though David demonstrated techniques for hollowing them out to make little boxes, held together by rare earth magnets.

Having mastered the basic shape, I decided to go for something more complicated. In this case an octagon, which is turned as a sort of barrel shape.

This involved more maths. But really the same sort of thing. This time I decided it was easier to pick a starting edge size, and figure out if the cylinder I had was large enough. I tried a couple of different starting numbers until I found the largest that would fit in the diameter I had. I’m sure there are simpler ways to figure it out, but I couldn’t be bothered to go looking them up.

Having split it, this shape actually has two positions it could be re-joined at that result in different shapes.
This first is this

Which is pretty cool, but I preferred the second option

Which is the one I glued it as. Again once you get to this kind of shape, the idea of using small rare earth magnets is a good one, because then you can rotate to any of the alignments you like, rather than fixing one forever.

I think next time I shall try one of the harder ‘star’ cross section pieces, that give pronounced spirals when formed as streptoheadrons. Or possibly have a go at hollowing out one of these shapes to make a small box. Not sure what you could put in such a box, but I guess the interesting part is the challenge of making it.