Previous analysis of the fossil-group/cluster RXJ1159+5531 with X-ray observations from a central Chandra pointing and an offset-North Suzaku pointing indicate a radial intracluster medium (ICM) entropy profile at the virial radius ($R_{\rm vir}$) consistent with predictions from gravity-only cosmological simulations, in contrast to other cool-core clusters. To examine the generality of these results, we present three new Suzaku observations that, in conjunction with the North pointing, provide complete azimuthal coverage out to $R_{\rm vir}$. With two new Chandra ACIS-I observations overlapping the North Suzaku pointing, we have resolved $\gtrsim$50\% of the cosmic X-ray background there. We present radial profiles of the ICM density, temperature, entropy, and pressure obtained for each of the four directions. We measure only modest azimuthal scatter in the ICM properties at $R_{\rm 200}$ between the Suzaku pointings: 7.6\% in temperature and 8.6\% in density, while the systematic errors can be significant. The temperature scatter, in particular, is lower than that studied at $R_{\rm 200}$ for a small number of other clusters observed with Suzaku. These azimuthal measurements verify that RXJ1159+5531 is a regular, highly relaxed system. The well-behaved entropy profiles we have measured for RXJ1159+5531 disfavor the weakening of the accretion shock as an explanation of the entropy flattening found in other cool-core clusters but is consistent with other explanations such as gas clumping, electron-ion non-equilibrium, non-thermal pressure support, and cosmic ray acceleration. Finally, we mention that the large-scale galaxy density distribution of RXJ1159+5531 seems to have little impact on its gas properties near $R_{\rm vir}$.

Accepted for publication in ApJ