Probably the simplest example --- $\{\ (x_1,...,x_n)\ |\ x_1+...+x_n=0\ \}$. Any choice of a basis distorts some symmetry...

Probably the simplest example --- $\{\ (x_1,...,x_n)\ |\ x_1+...+x_n=0\ \}$. Any choice of a basis distorts some symmetry...

As pointed out by Joe Silverman, this was in fact already mentioned in one of the previous answers. Let me still leave it, I think in this form it is sort of a "bare bones" example...