Reader Martin Raynsford took up the challenge, producing the following lovely model from cardstock, laser-cut, folded, and glued: Martin has graciously provided complete plans on his blog. In that earlier column, I suggested building an arrangement of 15 great circles. And now Math Monday has inspired a new addition to this sphere of constructions.

As a result, the web abounds with a variety of Fuller-inspired great circle constructions, such as this one consisting of 13 great circles, built by Bob Burkhardt using the classic 1960s geometrical construction toy, D-Stix. It took me about fifteen minutes to produce a model using this method, with a compass, four sheets of copier paper, and forty paper clips. In any case, Fuller wrote a great deal about different arrangements of great circles, especially the following 25-circle and 31-circle arrangements:įuller also devised a delightfully simple method to fold four great circles forming the edges of a spherical cuboctahedron from four circles of paper. Since, on the surface of a sphere a great circle is the shortest path, or geodesic, between two points, he dubbed his structures “geodesic domes.” Later on, even when they had different geometries, the name geodesic dome stuck. His original designs for domes involved bracing them solely with arcs of great circles.

I wrote an entire column on arrangements of great circles without once mentioning Buckminster Fuller.

Great circles book