Geodesic shapes

Geodesates, made up of lots of triangles, aren't regular shapes; if you look closely, most of the vertices are where 6 triangles meet, but some vertices only have 5 triangles.

Furthermore, where 6 triangles meet at one vertex, the six corners cannot all be 60° otherwise the geodesic would not be convex at that vertex. Therefore one or more of the angles are less than 60° and thus the triangle is not really equilateral.

Here are some closed geodesics, produced by spacing N nodes as far apart as possible on the surface of a sphere, then connecting nearby neighbors; 5-edge nodes are colored differently than the 6-edge nodes. N=72, N=100, N=200.