Mathesiusite, K-5(UO2)(4)(SO4)(4)(VO5)(H2O)(4), a new uranyl vanadate-sulfate mineral from Jachymov, Western Bohemia, Czech Republic, occurs on fractures of gangue associated with adolfpateraite, schoepite, cejkaite, zippeite, gypsum, and a new unnamed K-UO2-SO4 mineral. It is a secondary mineral formed during post-mining processes. Mathesiusite is tetragonal, space group P4/n, with the unit-cell dimensions a = 14.9704(10). c = 6.8170(5) angstrom. V = 1527.78(18) angstrom(3), and Z = 2. Acicular aggregates of mathesiusite consist of prismatic crystals up to 200 mu m long and several micrometers thick. It is yellowish green with a greenish white streak and vitreous luster. The Mohs hardness is similar to 2. Mathesiusite is brittle with an uneven fracture and perfect cleavage on (110} and weaker on {001}. The calculated density based on the empirical formula is 4.02 g/cm(3). Mathesiusite is colorless in fragments, uniaxial (-), with omega = 1.634(3) and epsilon = 1.597(3). Electron microprobe analyses (average of 7) provided: K2O 12.42, SO3 18.04, V2O5 4.30, UO(3)61.46, H2O 3.90 (structure), total 100.12 (all in wt%). The empirical formula (based on 33 O atoms pfu) is: K-4.87(U0.99O2)(4)(S1.04O4),(V087O5)(H2O)(4). The eight strongest powder X-ray diffraction lines are [d(obs) in angstrom (hkl) I-rel]: 10.64 (110) 76, 7.486 (200) 9, 6.856 (001) 100, 6.237 (101) 85, 4.742 (310) 37, 3.749 (400) 27, 3.296 (401) 9, and 2.9409 (510) 17. The crystal structure of mathesiusite was solved from single-crystal X-ray diffraction data and refined to R-1 = 0.0520 for 795 reflections with I > 3 sigma(I). It contains topologically unique heteropolyhedral sheets based on [(UO2)(4)(SO4)(4)(VO5)](5-) clusters. These clusters arise from linkages between corner-sharing quartets of uranyl pentagonal bipyramids, which define a square-shaped void at the center that is occupied by V5+ cations. Each pair of uranyl pentagonal bipyramids shares two vertices of SO4 tetrahedra. Each SO4 shares a third vertex with another cluster to form the sheets. The K. cations are located between the sheets, together with a single H2O group. The corrugated sheets are stacked perpendicular to c. These heteropolyhedral sheets are similar to those in the structures of synthetic uranyl chromates. Raman spectral data are presented confirming the presence of UO22+, SO4, and molecular H2O.