2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/35298I point out a symmetry, between equations of state for polytropic fluids, in the equation of motion of a spherically symmetric singular shell embedded in 4-d and 5-d vacuum spacetimes. In particular the equation of motion of a shell consisting of radiation has the same form as for a vacuum shell or domain wall.12 pages, 1 fig., typos and reference corrected. Submitted for publicationGeneral Relativity and Quantum CosmologyAstrophysicsHigh Energy Physics - Theorytext