Abstract: A domed self-supporting frameless building structure includes a plurality of monolithic, precast, elongated, concrete panels arranged in abutting edge to edge relationship with one another such that the panels are under compressive loadings in both the longitudinal and lateral directions. The longitudinal edges of each of such panels coincide with imaginary lines of longitude of a spherical or sphere-like shape. A plurality of circumferential courses of such panels are provided with the panels of any one such course being in abutting end-to-end relation with the panels of the next adjacent course. A tension ring surrounds the lower extremity of such dome and the lowermost ends of the panels of the lowermost course are in abutting relation with the ring thereby to assist in securing the panels together in the abutting edge to edge relationship.