Index

This shows that the sphere can be divided into spherical triangles
in an octahedral pattern (slide to the left) or an icosahedral
pattern (slide to the right). The triangles can then be flattened
out to make an actual regular polyhedron. We will need a
framework of definitions to capture these phenomena, and we will
need to prove that the answers to certain question do not change
depending on which pattern we use.