Regards
Narasimham
Locally, the within 2p, 4p subdivisions they may be geodesic arcs,
but for the entire spherical dome considered globally, the
nomenclature "geodesic dome" is clearly a misnomer.. with full
respects to Buckminster Fuller.
Best Regards
Narasimham
If the tubes alter direction often ( at arc lengths small compared
to the dome diameter ), then is it still a geodesic arc? On a
geodesic
line one would expect to see a continuous arc running for instance
between opposite points of the boundary of dome. At the side of the
basis icosahedron, the path changes direction. An assembly of
truncated geodesic arcs is not a geodesic path in a stricter sense
that such arcs make up non-geodesics or small circles.
Regards
Narasimham