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The CCAT observatory is a 25-m class Gregorian telescope designed for submillimeter observations that will be deployed at Cerro Chajnantor (similar to 5600 m) in the high Atacama Desert region of Chile. The Short Wavelength Camera (SWCam) for CCAT is an integral part of the observatory, enabling the study of star formation at high and low redshifts. SWCam will be a facility instrument, available at first light and operating in the telluric windows at wavelengths of 350, 450 and 850 mu m, and 2 mm. In order to trace the large curvature of the CCAT focal plane, and to suit the available instrument space, SWCam is divided into seven sub-cameras, each configured to a particular telluric window. A fully refractive optical design in each sub-camera will produce diffraction-limited images. The material of choice for the optical elements is silicon, due to its excellent transmission in the submillimeter and its high index of refraction, enabling thin lenses of a given power. The cryostat's vacuum windows double as the sub-cameras' field lenses and are similar to 30 cm in diameter. The other lenses are mounted at 4 K. The sub-cameras will share a single cryostat providing thermal intercepts at 80, 15, 4, 1 and 0.1 K, with cooling provided by pulse tube cryocoolers and a dilution refrigerator. The use of the intermediate temperature stage at 15 K minimizes the load at 4 K and reduces operating costs. We discuss our design requirements, specifications, key elements and expected performance of the optical, thermal and mechanical design for the short wavelength camera for CCAT.