A geodesic dome construction system utilizing a plurality of prefabricated panels having a triangular shape. Each panel includes a core of insulative material, an exterior cementitious face, an interior wall surface face, and edges of the core at an angle with respect to the faces. The exterior face includes an uncovered border portion and a wire mesh extending from the cementitious face into the border portion. The panels are assembled edge-to-edge to form a dome and the joints between panels reinforced with a wire mesh strip. The border portions and exposed wire mesh are covered with cured cementitious material forming a reinforced concrete rib along each joint.