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