  The Wythoff construction takes a $d$-dimensional polytope $P$, a subset $S$
of $\{0,..., d\}$ and returns another $d$-dimensional polytope $P(S)$. If $P$
is a regular polytope, then $P(S)$ is vertex-transitive. This construction
builds a large part of the Archimedean polytopes and tilings in dimension 3 and
4.
  We want to determine, which of those Wythoffians $P(S)$ with regular $P$ have
their skeleton or dual skeleton isometrically embeddable into the hypercubes
$H_m$ and half-cubes ${1/2}H_m$. We find six infinite series, which, we
conjecture, cover all cases for dimension $d>5$ and some sporadic cases in
dimension 3 and 4 (see Tables \ref{WythoffEmbeddable3} and
\ref{WythoffEmbeddable4}).
  Three out of those six infinite series are explained by a general result
about the embedding of Wythoff construction for Coxeter groups. In the last
section, we consider the Euclidean case; also, zonotopality of embeddable
$P(S)$ are addressed throughout the text.
