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, of late, by Raman spectroscopy. Determination of the crystal structure of these two polymorphs, using cryopowder and thin film X-ray diffraction techniques, has failed so far. Recently, we succeeded in sublimating α-H2CO3 and trapping the vapor phase in a noble gas matrix, which was analyzed by infrared spectroscopy. In the same way we have now investigated the β-polymorph. Unlike α-H2CO3, β-H2CO3 was regarded to decompose upon sublimation. Still, 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 (C(2v) and C(s)). In contrast to the earlier study on α-H2CO3, we do not find evidence for centrosymmetric (C(2h)) carbonic acid dimers here. This suggests that two monomers are entropically favored at the sublimation temperature of 250 K for β-H2CO3, whereas they are not at the sublimation temperature of 210 K for α-H2CO3.