Patterns On The Spherical Surface

This article is a sequel to that which the first author presented in Vol. 5, Nos. 3 & 4 (1990), of this Journal. In that article he displayed his work on patterns derived from skew networks. Here he extends this to patterns derived from subdivisions of the faces of other regular and semiregular polyhedra as these are projected onto the spherical surface. Some mathematical formulas are presented by the second author which can readily be used in a programmable calculator to obtain arcs, chord factors and radian measures for any frequency of subdivision and any suitable spherical radius. The first author made the papercraft models shown in the photos. The article ends with words of encouragement for artists, architects and engineers to use patterns in ornamental designs and in architectural projects.

Since the appearance of the article1 in this Journal the first author has been extensively engaged in developing new ways for making spherical models. He has also taken up an interest in using geometric patterns in a variety of designs. In his efforts to achieve some artistically beautiful effects, he has developed better ways to construct models still using only paper card stock for material as described in his published works2,3. A good successful model, however, can only be made when all the mathematical calculations have preceded the construction. Hence careful planning and preparatory drawings must be done before actual construction begins. The geodesic mathematics has all been done and is available for applications by anyone who wishes to study it. See the reference sources at the end of this article. The mathematics can often be very involved and hence often difficult to use.