Nowadays it =may= be the case that one can find this information on the internet, but when I read this it opened up a whole world.
The best of this describes the increasingly wooly territory outside of the often built icosahedral domes. There are octahedral domes, tetrahedral domes, and, gasp, irregular domes. It has been the case for me that irregular domes built on an octahedral geometry have suited my projects and the available materials better... and that's the point.
Get this book if you are good at maths and want to have a much wider solution space available for your projects.
If you can find windome.exe on the internet and a good rendering program, and then explore all the options, you may be able to skip the maths, or maybe even this book.