Descriptions by Simon Fraser Editorial comments by Roger's Connection are in italics.
To join up the ends of the ring, simply turn the ring 'inside out'; push the vertices towards the middle of the ring down, and it turns in on itself, allowing you to join the ends.
You can also turn the ring the other way (so the center vertices come up), and connect up again. This is simply the above structure turned over.
Here's an arch made of the same pentagonal shapes. It's just part of the circle shown above standing on the ends, with some tetrahedral feet added. It's not very stable either, because of the flex around the joins of the circle.
Finally, one of my favourite structures, this is two layers of pentagonal shapes, with three in each layer. The layers are then joined together by allowing the upper and lower points of the pentagons to share a ball, and adding three vertical struts. When complete, it is very rigid. You may think that one could continue building this upwards with many more layers, but no; because the angles are just slightly off, even a third layer is impossible to add.
Some quite dramatic bowl shapes can be built, starting from a rigid base and building outwards. This is just the shell of a large, 'relaxed' pyramid, upside down of course; it is build on a square base.
