Three-term unit arithmetic progression is not Euclidean Ramsey

The collinear set $\{0,1,2\}$ is not a Euclidean Ramsey set. In every dimension, coloring $x$ by $\lfloor 2\Vert x{\Vert }^2\rfloor$ modulo ten prevents a monochromatic congruent copy; the parallelogram law would force the corresponding three integer parts to have a second difference strictly between two and six, which cannot be divisible by ten.