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.