Geometrically, Spaceship Earth is a derivative of a pentakis dodecahedron. I
t is a Class 2 Frequency 16 Icosahedron, 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 silvered facets, with 954 partial or full flat triangular panels.
So...11,324