A kinetic model of vacancy diffusion induced by both the Gibbs-Thompson curvature effect and stress state of the Marks-Ioffe stereo-disclination in a hollow spherical particle is suggested to investigate the void evolution in hollow icosahedral particles. The obtained analytically vacancy concentration profile inside the hollow icosahedral particle is employed to derive numerically the evolution equation of void kinetics. It is shown that the scenario of void evolution in icosahedral particles strongly depends on the inner-to-outer radius ratio at the initial moment of time and on the value of dimensionless parameter α reflecting the contribution of a pressure-induced (drift) vacancy flux between the external and internal particle surfaces.