I have a polygon which I know is a rectangle, although it may be at any orientation:

![Example polygon](https://i.stack.imgur.com/vG265.png)

I want to shrink this polygon by a third of the width from two sides, so that I just get the strip in the middle - ending up with a result like the red area in this image:

![enter image description here](https://i.stack.imgur.com/Hyehc.png)

I can't think how to go about doing this easily. If I try and negatively buffer the polygon then it will be shrunk on all sides. I have many tens of thousands of these polygons to do - so obviously can't do them manually.

Any ideas? I have access to ArcGIS, QGIS and am relatively experienced at Python programming - if that helps.