# What's the smallest Hoberman sphere possible?

What is the smallest Hoberman sphere possible? Could it be possible on an atomic or molecular level?

Image courtesy of Hoberman Associates, Inc

I realize the issue with this will be the scissor joints. I am wondering how small these could be made and arranged. Would it be possible to create a functional Hoberman sphere with carbon nanotubes?

I am also curious if anyone has any opinion or knowledge about if it is possible to make a Hoberman “molecule” or rather a Hoberman sphere made of atoms? If so, what elements would make for the best Hoberman molecule? Could scissor joints be made functional at the molecular level both expanded and closed using something like redox reactions?

• It would improve the question if you add some references what a Hoberman sphere is, and what would distinguish it from any other type of molecular cages. What is a difference between a Hoberman molecule and a Hoberman sphere made of atoms? You have many related questions, with many unclear details. – Greg Aug 2 '17 at 2:32

Hoberman sphere shares the same topological features being an icosidodecahedron with a family of polyoxometalates called Keplerates $\ce{\{(\color{teal}{Mo|W})_72\color{orange}{M}_30\}}$ ($\ce{\color{orange}{M} = Fe,Cr,V}$, anionic residues and alkali metal cations are removed for clarity) ([1, 2]):

Also, there is a cluster $\ce{[\color{blue}{La}_20\color{green}{Ni}_30(IDA)30(CO3)6(NO3)6(OH)30(H2O)12](CO3)6 * 72H2O}$ (IDA - iminodiacetate $\ce{C4H5NO4}$) consisting of an icosidodecahedron of Ni(II) Ions encapsulating an inner La(III)-dodecahedron [3]:

The problem is, these structures only resemble the symmetry, but not the expandability of Hoberman sphere. Currently there are many attempts of creating nanomachines with mechanically active molecular assemblies, but I didn't find any working models close to Hoberman structures (yet).

Also, some "spherical" viruses such as Cowpea chlorotic mottle virus (CCMV) with a structure of truncated icosahedron, which is significantly larger than Keplerates ($\pu{28 nm}$ (CCMV) vs. $\pu{3.2 nm}$ (average Keplerate)), can undergo swelling (pH < 6.5) and expansion (pH > 6.5), and show pH and metal ion dependent polymorphism [4, 5]

as a result of deprotonation of carboxyl moieties at the inter-capsomere contacts, leading to electrostatic repulsion that opens out the structure but falls short of complete disassembly through preservation of interwoven carboxyl/protein links between capsomeres.

Don't forget that "there's plenty of room at the bottom", so Hoberman sphere can possibly be a real working entity at molecular scale.

### Bibliography

1. Botar, B.; Ellern, A.; Hermann, R.; Kögerler, P. Angewandte Chemie International Edition 2009, 48 (48), 9080–9083. DOI 10.1002/anie.200903541.
2. Schäffer, C.; Merca, A.; Bögge, H.; Todea, A. M.; Kistler, M. L.; Liu, T.; Thouvenot, R.; Gouzerh, P.; Müller, A. Angewandte Chemie 2009, 121 (1), 155–159. DOI 10.1002/ange.200804496.
3. Kong, X.-J.; Ren, Y.-P.; Long, L.-S.; Zheng, Z.; Huang, R.-B.; Zheng, L.-S. J. Am. Chem. Soc. 2007, 129 (22), 7016–7017. DOI 10.1021/ja0726198.
4. Speir, J. A.; Munshi, S.; Wang, G.; Baker, T. S.; Johnson, J. E. Structure 1995, 3 (1), 63–78. DOI 10.1016/S0969-2126(01)00135-6.
5. Kovacs, F.; Tarnai, T.; Guest, S. D.; Fowler, P. W. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 2004, 460 (2051), 3191–3202. DOI 10.1098/rspa.2004.1344.