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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?

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  • $\begingroup$ 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. $\endgroup$ – Aant Jul 11 '12 at 19:53
  • $\begingroup$ 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. $\endgroup$ – porphyrin Aug 5 '16 at 13:39
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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.

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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.

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