On the strong non-rigidity of certain tight Euclidean designs

We study the non-rigidity of Euclidean tt-designs, namely we study when Euclidean designs (in particular certain tight Euclidean designs) can be deformed keeping the property of being Euclidean tt-designs. We show that certain tight Euclidean tt-designs are non-rigid, and in fact satisfy a stronger form of non-rigidity which we call strong non-rigidity. This shows that there are plenty of non-isomorphic tight Euclidean tt-designs for certain parameters, which seems to have been unnoticed before. We also include the complete classification of tight Euclidean 2-designs.