This can be done in 1 or 2 pitches.
Start up a small dihedral (5.6) or take an easier start to the right (5.5). Follow the crack over a bulge, then onto the large face. Keep following the right crack to the roof. Either turn the roof at a dihedral to the left (red), which is the same finish to East of the Sun or take a crack straight up from the route.
Descent: walk off to the right side of the Dome.