Geodesic Tessellations with Maximal Identical Equilateral Triangles

Geodesic tessellations are typically derived from projective and spherical division methods that provide a wide range of component variability. The computational requirements are straightforward and can be applied to all three topological classes. This paper provides an alternate optimization method using equilateral triangle chains that requires special computational techniques. When applied to any class the resulting spherical surfaces have one identically sized equilateral triangle that comprises ~50% of the total number of triangles. The method utilizes the underlying the fact that fixed spherical points of symmetry can be maintained while the tessellation grid has rotational freedom. This approach provides architects and designers with a new pattern dimension to apply to aesthetic enhancements.