Techniques are described for constructing geodesic dome structures. For example, a method includes connecting a set of panels to form a geodesic dome. The panels have surface contours that conform to a surface contour of a geodesic dome having a dimension larger than a dimension of the geodesic dome formed by the panels. Another method includes attaching flanges to a set of permanent structure members that form a permanent geodesic dome structure. The method further includes fastening a set of panels to the flanges. The panels enclose the geodesic dome structure to form the geodesic dome. The techniques described may allow the construction of a geodesic dome structure of precisely controlled dimensions with relatively small numbers of people and little strenuous labor.