The design of the randome provides a spherical or near-spherical structure that is made of elements that are simple and inexpensive to manufacture and to assemble. Unlike previous geodesic dome designs, which required exacting measurements and were generally limited to spherical forms, the randome is a structure that is versatile in form and not restricted to the form of an icosahedron. The randome can be easily assembled without requiring complex mathematical calculations and without having to arrange the elements in a pattern along predetermined great circle gridlines. As the name implies, the randome design functions not so much as a design template, but as a modular construction system with a high degree of flexibility.