Step 1: Materials
You will need only these things:
1. Masking tape;
2. 30 glass triangles A, 10 glass triangles B;
3. Sharp blade;
4. Colorless silicone.
The glass has to be cut in two triangles, like the template showed below. 30 triangles called A, and 10 triangles called B. You can scale the triangles together up or down, and use any thickness or glass color that you like. The triangles can be cut of a rectangle, like showed below, saving material. You can learn how to cut glass here, or to order it from a glass professional. Ask for the most accurate cut, because the errors will add at the end.
If you like, you could use another materials too: plastic, acrylic, pvc, wood... You can try also another types of adhesive instead silicone: two-part epoxy, pvc glue, gorilla glue, etc. Each of them will have their own different features and have to be tested before you start.
To make a dome with 40 cm of diameter, the base of the triangles will have 123,5 mm each. If you scale up the figure, the dome will be higher, if you scale down it will be smaller.
Step 2: Protecting the Glass
Mask the edges of all the glass triangles to protect then from the silicone excess in the joints. Remember: it's very difficult to clean the cured silicone from the glass. It's far more easy to protect it first. Cut the tape close to the edge with a sharp blade.
Step 3: Making the Hinges
Separate the A triangles. Turn the tape covered triangles to the side of the unsheltered glass and apply more tape along the two smaller edges of them, leaving half of the tape exposed to attach another triangle, making a hinge between them. Cut the excess of tape.
When five of the A triangles are united with tape hinges along the small edges of them, raise then until the two remaining edges touch together and join them with tape, making a pentagonal pyramid.
Step 4: Filling the Joints
Now there are only exposed glass between the sides of the masked glass triangles. Fill the joints with silicone and remove the excess with a piece of metal or plastic. Repeat the process in all joints and make six pentagonal pyramids similarly. Leave the pieces aside until the silicone was totally cured (around 24 hours).
Step 5: Joining the Parts
Get two of the pyramids and link then using two B triangles, in the way previously described. Look carefully to the images below. One of the pyramids must be united with two B triangles, like showed in the images below. Wait more 24 hours until the silicone was cured.
Step 6: Joining the Parts - Final
Now it's time to close the dome, uniting the missing parts. Link the two bigger modules with two more B triangles, and join the remainder module behind. The last pyramid on the top is the most difficult to fit, because there are a sum of errors in the measures. May be necessary some glass sanding and fine adjustments.
Step 7: Removing the Tape - Interior
When all silicone joints are totally cured, remove the inside tape hinges.
Step 8: Removing the Tape - Exterior
Now remove the outside tape, showing all the glory of the dome.
Step 9: Finishing
Cut the excess of silicone with a sharp blade and clean the glass. Now you have an exotic and sophisticated piece of conversation. Show it to your friends!