Geodesic dome Johnson solids, Archimedean solids, and Catalan solids. These structures may have some faces that are not triangular, being squares or other polygons. In 1975, a dome was constructed at the South Pole, where its resistance to snow and wind loads is important. On October 1, 1982, one of the most famous geodesic domes, Spaceship Earth at Epcot in Walt Disney World Resort in Bay Lake, Florida, just outside of Orlando, Florida, opened. The building and the ride inside of it are named with one of Buckminster Fuller's famous terms, Spaceship Earth, a world view expressing concern over the use of
Solving the geodesic equations curve γ("s") in formula_1 and formula_5 are the Christoffel symbols. The Christoffel symbols are functions of the metric and are given by: where the comma indicates a partial derivative with respect to the coordinates: As the manifold has dimension formula_8, the geodesic equations are a system of formula_8 ordinary differential equations for the formula_8 coordinate variables. Thus, allied with initial conditions, the system can, according to the Picard–Lindelöf theorem, be solved. One can also use a Lagrangian approach to the problem: defining and applying the Euler–Lagrange equation. As the laws of physics can be written in any coordinate system, it