  Suppose that a compact $r$-dimensional torus $T^r$ acts in a holomorphic and
Hamiltonian manner on polarized complex $d$-dimensional projective manifold
$M$, with nowhere vanishing moment map $\Phi$. Assuming that $\Phi$ is
transverse to the ray through a given weight $\boldsymbol{\nu}$, associated to
these data there is a complex $(d-r+1)$-dimensional polarized projective
orbifold $\hat{M}_{\boldsymbol{\nu}}$ (referred to as the $\boldsymbol{\nu}$-th
\textit{conic transform} of $M$). Namely, $\hat{M}_{\boldsymbol{\nu}}$ is a
suitable quotient of the inverse image of the ray in the unit circle bundle of
the polarization of $M$. With the aim to clarify the geometric significance of
this construction, we consider the special case where $M$ is toric, and show
that $\hat{M}_{\boldsymbol{\nu}}$ is itself a K\"{a}hler toric obifold, whose
moment polytope is obtained from the one of $M$ by a certain "transform",
operation (depending on $\Phi$ and $\boldsymbol{\nu}$).
