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CCAT will be a 25 m diameter submillimeter-wave telescope that will operate inside a dome located on Cerro Chajnantor in the Atacama Desert. The telescope must have high aperture efficiency at a wavelength of 350 microns and good performance out to a wavelength of 200 microns. A conceptual design for a carbon fiber reinforced plastic (CFRP) truss and primary reflector support truss has been developed. This design yields a telescope with a net wave front error of <10 microns using a lookup table to adjust the segment actuators to compensate for gravitational deflections. Minor corrections may be required to compensate for the expected 20 C temperature excursions. These can be handled using a coarse lookup table.