Twenty years ago two different polymorphs of carbonic acid, α- and β-H2CO3, were isolated as thin, crystalline films. They were characterized by infrared and, lately, by Raman spectroscopy. Determination of the crystal structure of these two polymorphs, using cryo-powder and thin film X-ray diffraction techniques, has failed so far. Recently, we succeeded in sublimating α-H2CO3 and trapping the vapour phase in a noble gas matrix, which was analyzed by infrared spectroscopy. In the same way we have now investigated the β-polymorph. Even though β-H2CO3 was regarded to decompose upon sublimation, by contrast to α-H2CO3, we have succeeded in isolation of undecomposed carbonic acid in the matrix and recondensation after removal of the matrix here. This possibility of sublimation and recondensation cycles of β-H2CO3 adds a new aspect to the chemistry of carbonic acid in astrophysical environments, especially because there is a direct way of β-H2CO3 formation in space, but none for α-H2CO3. Assignments of the FTIR spectra of the isolated molecules unambiguously reveal two different carbonic acid monomer conformers (C2v and Cs). By contrast to the earlier study on α-H2CO3 we do not find evidence for centrosymmetric (C2h) carbonic acid dimers here. This suggests that two monomers are entropically favoured at the sublimation temperature of 260 K for β-H2CO3, whereas they are not at the sublimation temperature of 210 K for α-H2CO3.