  Sizable single-crystalline samples of
Ca$_{10}$(Pt$_3$As$_8$)((Fe$_{1-x}$Pt$_x$)$_2$As$_2$)$_5$ (the 10-3-8 phase)
with 0$\leq x<$0.1 have been grown and systematically characterized via X-Ray
diffraction, magnetic, and transport measurements. The undoped sample is a
heavily doped semiconductor with no sign of magnetic order down to 2 K. With
increasing Pt content, the metallic behavior appears and superconductivity is
realized for $x\geq$0.023. $T_{\rm c}$ rises to its maximum of approximately
13.6 K at the doping level of $x\sim$0.06, and then decreases for higher $x$
values. The electronic phase diagram of the 10-3-8 phase was mapped out based
on the transport measurements. The mass anisotropy parameter $\Gamma\sim$10
obtained from resistive measurements in magnetic fields indicates a relatively
large anisotropy in the iron-based superconductor family. This strong 2D
character may lead to the absence of magnetic order. A linear $T$-dependence of
susceptibility at high temperature is observed, indicating that spin
fluctuations exist in the underdoped region as in most of the Fe-pnictide
superconductors.
