We report on a new class of solutions of black hole accretion disks that we have found through three-dimensional , global , radiative magnetohydrodynamic simulations in general relativity . It combines features of the canonical thin , slim and thick disk models but differs in crucial respects from each of them . We expect these new solutions to provide a more realistic description of black hole disks than the slim disk model . We are presenting a disk solution for a non-spinning black hole at a sub-Eddington mass accretion rate , \dot { M } = 0.6 \dot { M } _ { Edd } . By the density scale-height measure the disk appears to be thin , having a high density core near the equatorial plane of height h _ { \rho } \sim 0.1 r , but most of the inflow occurs through a highly advective , turbulent , optically thick , Keplerian region that sandwiches the core and has a substantial geometrical thickness comparable to the radius , H \sim r . The accreting fluid is supported above the midplane in large part by the magnetic field , with the gas and radiation to magnetic pressure ratio \beta \sim 1 , this makes the disk thermally stable , even though the radiation pressure strongly dominates over gas pressure . A significant part of the radiation emerging from the disk is captured by the black hole , so the disk is less luminous than a thin disk would be at the same accretion rate .