There is an increasing number of theoretical predictions suggesting that many nuclear states should be characterised by spatial tetrahedral and/or octahedral symmetries. One of the most crucial points in this domain of research is how to demonstrate the existence of this new exotic quantum mechanism through experiment. We discuss in some detail how the rotational properties of tetrahedral nuclei can be used to pin down the presence of the tetrahedral symmetry in sub-atomic universe.

PACS numbers: 21.10.--k, 21.60.--n, 21.60.Fw