This 18-story high geodesic sphere is a pentakis dodecahedron, with each of the 60 isosceles triangle faces divided into 16 smaller equilateral triangles (with a bit of fudging to make it rounder). Each of those 960 flat panels is sub-divided into four triangles, each of which is divided into three isosceles triangles to form each point. In theory, there are 11,520 total isosceles triangles forming 3840 points. In reality, some of those triangles are partially or fully nonexistent due to supports and doors; there are actually only 11,324 of them, with 954 partial or full flat panels.
The cladding was designed so that when it rains, no water pours off the sides onto the ground. (All water is "absorbed" through one inch gaps in the facets and is collected in a gutter system - and finally channeled into the World Showcase Lagoon.)
Construction took 26 months and 40,800 labor hours to build.
You can see more about Spaceship Earth here.
You can see more ABC Wednesday here.