Synclastic hollow core building panels are employed to form dome-like structures. The synclastic curve allows the panels to be lightweight, yet capable of carrying the weight of the structural loads. When combined, the panels create a sphere or a section of a sphere for enclosing space, with optional egress, skylight, and foundation portals incorporated into the structure without disturbing the spherical curvature of the interior or exterior surfaces. The spheres or sphere sections require no additional framing; the panels themselves are the frame. Workers with only the basic assembly skills can construct a sphere or sphere sections using these panels.