Google search of sphere tessellation led me to igloos :-) Here are some links:

http://th.if.uj.edu.pl/~odrzywolek/homepage/publications/PDF/igloos%20final.pdf

http://cs.stmarys.ca/~dawson/images4.html

http://gnomonique.fr/trisph/index_en.htm

French version:
http://gnomonique.fr/trisph/lisezmoi.pdf

ftp://skipjack.soc.lib.md.us/gutenberg/1/9/7/7/19770/19770-pdf.pdf

(Still working on the igloo. I think I just need a sphere and some planes at angles of PI/2, PI/3, and PI/5, (90, 60, 36 degrees), maybe.)

- Brian

Not sure that it will be all that useful in Sydney, Australia, but the results of your work should be lots of fun.

Mike.

Cool, i'm interested to see how this turns out