  The dynamic electric dipole polarizabilities of the $5s^2~^1S_0$,
$5s5p~^3P_{0}$, and $5s5p~^3P_2$ states for Cd atoms are calculated using the
relativistic configuration interaction plus many-body perturbation theory
method. The magic wavelengths for the $5s^2~^1S_0\rightarrow 5s5p~^3P_{0}$ and
$5s^2~^1S_0\rightarrow 5s5p~^3P_2$ transitions within a range of 300-500 nm are
identified. The possibility of achieving triple magic trapping for the
transitions $5s^2~^1S_0\rightarrow5s5p~^3P_{0}$ and
$5s^2~^1S_0\rightarrow5s5p~^3P_2$ is investigated. It is found that no common
magic wavelength could be identified for achieving triple magic trapping with
the linearly polarized light. However, if the degree of ellipticity is between
$0.358$ and $1$, the triple magic trapping can be achieved at 419.88 nm for the
$5s^2 ~ ^1S_0\rightarrow 5s5p~^3P_2$ ($M_{i}=\pm2$) and
$5s^2~^1S_0\rightarrow5s5p~^3P_{0}$ transitions.
