Abstract: A modular geodesic dome construction simultaneously optimizes vertex positioning to be equidistant from a central point and minimizes a number of uniquely shaped triangular panels utilized in construction. The dome construction includes a plurality of triangular panels being coupled together along sides of the triangular panels forming a geodesic polyhedron structure. Each side of each of the triangular panels has a length corresponding to an associated one of only five length factors times a radius of the geodesic polyhedron structure. Additionally, the five distinct shapes of the triangular panels are either isosceles or equilateral triangles.