Star Antiprism

 

3d printed Star Antiprism on 2d drawing used for working out the geometry and

then making the 3d cad file. This is based on a 9 sided figure.

Hi

For a few months I've been working on a form of structure which is a sort of up-polygonization, that is making circles into polygons, and building different structures from them, as per this post . Recently I submitted an abstract about them to a conference, so hope to be writing a formal article about them soon.

Anyway, in preparation for that, I've been doing more maths calcs about the constructions including some on antiprism geometry.  And that bought on the idea of a different type of antiprism, one based on a star or fractional polygon. At first I couldn't find references to them on the web and ploughed on with 2d cad to work out the geometry, 3d cad to make an STL file, and then sd printing to make a demo model. I'm happy with the result which is a thin-walled shell antiprism stack.

It turns out that wikipedia covers star antiprisms  here , and this article shows a stack of star antiprisms.

Anyway, the stack I made seems very interesting, for example the stack reverts to a simple polygon at certain heights, and it has triangles on the outside and quadrilaterals inside. As well, its possible the outside of the shape could be made with origami. This site shows a similar pattern. I plan to play around with it and see if I can come up with some more designs based on it. 

Regards

Steve Nurse