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Layered Ca₁₀Pt₄As₈(Fe₂As₂)₅ is unique because it is the only-known system that contains an metallic spacer between adjacent Fe₂As₂ layers and becomes optimally superconducting without chemical doping at ambient pressure. However, the unsolved crystal structure limits our understanding of structure-property relationship. Using electron diffraction and high-resolution scanning transmission electron microscopy (STEM), we are able to directly determine the structure of this superconductor: it forms a monoclinic structure (P 2 1/n) with the unit cell along the c direction doubled compared that found previously, i.e., c = 20.18 Å. Stacking faults along c-axis are commonly observed in the crystal. With the establishment of the crystal structure, the unique transport properties of our superconducting Ca₁₀Pt₄As₈((Fe_1-xPt_x)₂As₂)₅ (x ~ 0.05) single crystals with T_c = 34 K can be explained.