# Are all cubic point groups encountered?

My symmetry lecture notes state that there are seven high-symmetry 3D point groups, which have more than one rotation axis of order greater than 2: $T$, $T_d$, $T_h$, $O$, $O_h$, $I$, $I_h$. I sometimes see them called the “cubic point groups”.

My point is: most molecules (or molecular fragments) I have encoutered in these groups are always $T_d$ (tetrahedral) or $O_h$ (octahedral). What are examples of molecules in the other groups?

• Just a quick correction: I would only call the tetrahedral and octahedral point groups cubic (which means they're compatible with a cubic crystal lattice) - the icosahedral point groups are not. – Aant Jul 11 '12 at 19:53
• have a look at molecule-viewer.com where there are examples of molecules from all point groups. However, its designed test your ability to work out point groups not just look up examples. – porphyrin Aug 5 '16 at 13:39

I refer you to the second link in my answer for How does one recognized Td/Oh symmetry in molecules?, which (according to the abstract) describes some high symmetry species of unusual point groups $T$, $O$ and $I$. Additionally, the molecule [6.6]chiralane has $T$ symmetry.
Buckminsterfullerene is a well known $I_{h}$ symmetric molecule.
Don't know of any $T_h$ molecules but I'm confident they can be devised.
At least six of these seven point groups been encountered. You can see examples on the Otterbein symmetry gallery. The one that's missing from this gallery is $I$, although as Richard pointed out, people have theoretically predicted some molecules with this symmetry to be stable.