Quote:

Let $\displaystyle X=\{A,\ B,\ C, \ D\}$ with $\displaystyle d(A,D)=2$, but all other distances equal to 1.

d is a metric.

Prove that the metric space X is not isometric to any subset of $\displaystyle \mathbb{E}^n$ for any n.

Hint: can you realise $\displaystyle X$ as a subset of a sphere $\displaystyle S^2$ of appropriate radius, with the spherical "great circle" metric?

I think I have to take two points in $\displaystyle X$ and show that any mapping from $\displaystyle X$ to $\displaystyle \mathbb{E}^n$ would result in a different distance between them.