  Let $X$ be an $n$-point subset of a Euclidean space and $0 < a < 1$. The
classical theorem of Schoenberg implies that the snowflake space $X^a$ can be
isometrically embedded into Euclidean space. In the paper we show that points
in the image of such an embedding always are in general position. As
application we prove the analogue of Schoenberg's result for quotients of
Euclidean spaces by finite groups.
