Start at the outside bottom of the hemisphere, and make a “ring” of triangles, leaving one missing wherever it is that you would like a doorway. It is helpful to place a panel there and remove it, just to check alignments. Triangles will come together above this opening, so they do need to fit together well (or well enough).

Work on the second level ring. Note that it is not strictly one ring followed by another, as it is a geodesic dome. But we are building ground up. Fill in triangles where appropriate.

in this photo you can see at the right, a small red model of the dome.  That is a half of a "Ball of Whacks" with markings on it to map out the triangle placement.

Once things get high enough, be extremely careful. (Actually, don’t wait until then to be extremely careful.) These panels are slippery, since they are made of ice. If you drop one, you can break your foot or leg. Wear a hard hat. Wear steel-toed boots. Do not ignore the large amount of potential energy stored in an overhead suspended object.

As the dome comes together, the panels lean inwards over you. When a newly added panel has two adjacent panels already in place, it can be placed with a little bit of snow mortar easily. If there are not adjacent panels, some temporary support may be necessary to hold the panel in position as it begins to freeze in place, while you place an adjacent panel, and the two new panels can support each other and freeze in place together. Do not let one panel stick out in space and freeze in place by itself - it is necessary to place the second one to get the correct angle. It is exceedingly difficult to do this by eye alone. 

You can check that you are on the spherical radius using the same rope used to mark out the perimeter in the site prep step. Correct error as you go - small continuous error correction will be much more successful than a large single attempt, which actually may not be possible after a certain point.

Continue around and up until you have only two panels left to place at the apex. The panels over the door opening should have met naturally, and formed their own support, with no additional structure necessary.

Place the two apex panels. Do this from the inside. Rest the two remaining panels on the top of the dome, near where they will rest in the final configuration. They will individually fit sideways through the hole, which is two panels across, and then can be rested on top of the dome. once outside the dome, slide them carefully in place. If done accurately enough, the two panels will simply meet and fill the hole. A little snow mortar can be slathered into the joints to help solidify their position.

That’s it, the dome is done!

If you were careful in the site prep step, and managed to hold all tolerances very tightly, the doorway opening can be aligned such that if you stand in the center of the dome, it will frame the extents of the motion of the star Thuban (or any other fairly fixed celestial object of your choosing). Don’t forget to take into account your height (eye-level). The alignment is only valid for high priests of this height. I was not successful in holding close enough to an ideal hemisphere for this to work. But, I have high hopes for version 2.