ABSTRACT
Previous chapters have presented techniques for evenly distributing points on the surface of a sphere and using them to create triangular, diamond, or hex-pent tessellations. This chapter presents a series of visual and statistical metrics comparing those subdivision schemas. There are common treads between each metric and each provides a partial answer to the question of which is better for a particular application. They include minimizing the number of different member lengths, dihedral or surface angles or making face areas as equal as possible. Comparison metrics include kissing-touching, equalness, minimum variation in triangle areas, face acuteness, centroids, and convex hulls. Statistical analysis and visual comparisons using stereographic projection of spherical caps at vertex locations is demonstrated. The overwhelming use of spherical icosahedrons, or its Catalan dual the rhombic triacontahedron, as references for spherical design are easily justified.
