[Co-3(HCOO)(6)](CH3OH)(H2O) (1), the isostructural analogue of the porous magnet of coordination framework [Mn-3(HCOO)(6)](CH3OH)(H2O), and its desolvated form [Co-3(HCOO)(6)] (2) were prepared and characterized by X-ray and neutron diffraction methods, IR, thermal analyses, and BET, and their magnetic properties were measured. The parent compound, 1, crystallizes in the monoclinic system, space group P2(1)/c, a = 11.254(2) Angstrom, b = 9.832(1) Angstrom, c = 18.108(3) Angstrom, beta = 127.222(2)degrees, V = 1595.5(4) Angstrom(3), Z = 4, R1 = 0.0329 at 180 K. It possesses a unit cell volume that is 9% smaller than [Mn-3(HCOO)(6)](CH3OH)(H2O) due to the smaller radius of CO2+ ion. Compared with the parent compound 1, the desolvated compound 2 has slightly larger lattice with cell parameters of a = 11.2858(4) Angstrom, b = 9.8690(4) Angstrom, c = 18.1797(6) Angstrom, beta = 127.193(2)degrees, V = 1613.0(1) Angstrom(3), R1 = 0.0356 at 180 K. The cell parameters of 2, obtained from neutron powder data at 2 K, are a = 11.309(2) Angstrom, b = 9.869(1) Angstrom, c = 18.201(3) Angstrom, beta = 127.244(8)degrees, V = 1617.3(5) Angstrom(3). The pore volume reduces from 33% to 30% by replacing Mn by Co. The material exhibits a diamond framework based on Co-centered CoCo4 tetrahedral nodes, in which all metal ions have octahedral coordination geometry and all HCOO groups link the metal ions in syn-syn/anti modes. It displays thermal stability up to 270 degreesC. The compound easily loses guest molecules without loss of crystallinity, and it partly reabsorbs water from the atmosphere. Significant N-2 sorption was observed for the desolvated framework suggesting that the material possesses permanent porosity. The magnetic properties show a tendency to a 3D long-range magnetic ordering, probably antiferromagnetic with a spin canting arrangement below 2 K.