Light scattering and viscosity measurements were made on anionically polymerized four-arm star polystyrene samples with weight-average molecular weights M-w of 8.5 x 10(4) to 3.1 x 10(6) in cyclohexane at different temperatures to determine the mean-square radius of gyration [S-2], the second and third virial coefficients (A(2) and A(3)), and the intrinsic viscosity. The values of A(3) at the Theta point (34.5 degrees C), where A(2) for any sample was essentially zero, were about 5 x 10(-4) cm(6) mol g(-3) and yielded a value of 4 x 10(-45) cm(6) for the ternary cluster integral. It was shown that although the binary cluster approximation breaks down for A(3) near Theta, it holds for [S-2] and A(2), as is the case with linear chains, if the binary cluster integral is replaced by a linear combination of the binary and ternary cluster integrals. The expansion factor alpha(S)(2) for [S-2] and that for the intrinsic viscosity plotted against the excluded-volume parameter z in the coil limit for M-w > 8 x 10(5) came close to the known relations for linear polystyrene of high molecular weight in cyclohexane. On the other hand, the relation between the interpenetration function Psi and alpha(S)(3) for the star polymer appeared far above that for the linear chain at temperatures above Theta. These experimental results for alpha(S)(2) and Psi were quantitatively explained by the interpolation formulas constructed in this work.