Twinning has been recognized to be an important microstructural defect in nanoscale materials. Periodically twinned SiC nanowires were largely synthesized by the carbothermal reduction of a carbonaceous silica xerogel prepared from tetraethoxysilane and biphenyl with iron nitrate as an additive. The twinned β-SiC nanowires, with a hexagonal cross section, a diameter of 50-300 nm and a length of tens to hundreds of micrometers, feature a zigzag arrangement of periodically twinned segments with a rather uniform thickness along the entire growth length. Computer simulation has been used to generate three-dimensional atomic structures of the zigzag columnar twin structure by the stacking of hexagonal discs of {111} planes of SiC. A minimum surface energy and strain energy argument is proposed to explain the formation of periodic twins in the SiC nanowires. The thickness of the periodic twinned segments is found to be linearly proportional to the nanowire diameter, and a constant volume model is proposed to explain the relation.