A note on diameter-Ramsey sets

A finite set $A\subset {\mathbb{R}}^d$ is called $\mathit{\text{diameter-Ramsey}}$ if for every $r\in \mathbb{N}$, there exists some $n\in \mathbb{N}$ and a finite set $B\subset {\mathbb{R}}^n$ with $\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}(A)=\mathrm{d}\mathrm{i}\mathrm{a}\mathrm{m}(B)$ such that whenever $B$ is coloured with $r$ colours, there is a monochromatic set $A’ \subset B$whichiscongruentto$A$\mathrm{.}Weprovethatsetsofdiameter$1$ with circumradius larger than $1\mathrm{/}\sqrt{2}$ are not diameter-Ramsey. In particular, we obtain that triangles with an angle larger than ${135}^{\circ }$ are not diameter-Ramsey, improving a result of Frankl, Pach, Reiher and R"odl. Furthermore, we deduce that there are simplices which are almost regular but not diameter-Ramsey.