An exact expression for the emissivity of an ideally diffuse, gray, isothermal, spherical cavity is derived directly, making no geometrical approximations, and is shown to agree with the results of DeVos, Gouffé, and Sparrow and Jonsson, as compared by Fecteau. It appears that, even under ideal conditions, the spherical configuration is the only one that will have uniform isotropic emissivity over a wide angle, approaching a full hemisphere, across the entire aperture.
Fred E. Nicodemus, "Emissivity of Isothermal Spherical Cavity with Gray Lambertian Walls," Appl. Opt. 7, 1359-1362 (1968)