Thanks for asking. One difference is that a dome is an incomplete (truncated) sphere. 'Geodesic' implies that the sphere's polygons are generated by successive subdivisions of the faces of an icosahedron, dodecahedron or tetrahedron. Triangular faces can be grouped into diamonds, or hexes and pents (think soccer ball). Geodesics would be a subset of low-polygon spheres. It's been a while since I've seen Bryce, but IIRC those are (octahedral) geodesic spheres. Dome 4.6 can generate a wide variety of geodesics. If your interested, it's available at http://www.cris.com/~rjbono/html/domes.html