Cover the geodesic dome framework with the fine wire mesh by securing the mesh to the struts with zip-ties or wire ties. The mesh can be cut beforehand into the correct size triangles (slightly larger than the triangles on the dome), then tied up one at a time. Layer the mesh two or three layers thick, if cost allows.
Mix up the mortar cement in a motorized mixer and carefully spread it around the bottom of the dome. Taper the concrete so that it can be cured and layered, moving up the sides of the dome as more concrete is added. Complete the bottom "ring" of concrete from the ground to about a foot up the side of the dome. Let it cure for about an hour, then add another foot-high ring. This prevents cracking as the concrete dries, and creates a solid barrier. Continue to spread the concrete, avoiding the openings for windows, until the top of the dome is reached. Let the structure cure for a minimum of 48 hours and check it for cracks.
Apply another layer of concrete, if desired, or seal the roof with several gallons of concrete sealer. Spread the sealer like paint onto the concrete surface and allow it to dry completely. Add several more coats until there is no more sealer. This added step of sealing the concrete will make the home much more resistant to weathering and pitting.