Geodesic Dome

I finally realized why a geodesic dome is called that. The points inside each triangular icosahedral face are constructed on the intersections of geodesics connecting equally spaced points on the edges of each icosahedral face. It is not obvious that three geodesics intersect at a point. These geodesics cause forces to be purely compressive along the edge structural members, probably explaining the dome's strength.

Could a geodesic dome be constructed from an octahedron instead of an icosahedron?