The tensegrity structure is light and convenient to connect. It can satisfy the lightweight requirements of large-scale space structures. A tensegrity unit with equal cable length is easier to produce, more convenient to install and has better symmetry. Based on the properties of the tensegrity basic unit, studies the characteristics of the tensegrity unit with equal cable length. Analyze the functional relationship between bars number \({\text{p}}\) (main fractal parameter) and the connection mode of stay cables \({\text{j}}\) (auxiliary fractal parameter) when forming a stable unit with equal cable length, and find the variation law of geometric shape parameters of unit with the changing main fractal parameter and auxiliary fractal parameter through the self-stress balance analysis. The results show that all geometric parameters of unit with equal cable length except height increase with the increase of fractal parameters, and the height changes in five regions with the increase of fractal parameters, which includes two constant value areas.