To get any useable space in a tipi, it would have to be pretty tall. One site I found ( http://www.coureurdebois.com/teepee.html
) sold a 3-4 person tipi that was 14 feet tall. That's a big umbrella to lug around.
Maybe something like a Hoberman dome ( http://www.hoberman.com/fold/discoverdome/domes_all.htm
) could be made for camping. I found a couple of refernces to a tent he made but never found a picture of the tent itself. Maybe this already exists; I don't know.