  We show that any finite affinely independent set can be isometrically
embedded into a regular polygonal torus, that is, a finite product of regular
polygons. As a consequence, with a straightforward application of
K\v{r}\'{i}\v{z}'s theorem, we get an alternative proof of the fact that all
finite affinely independent sets are Ramsey, a result which was originally
proved by Frankl and R\"{o}dl.
