Jim Propp asks about the uniqueness of the projective plane of order 2. LEMMA: Up to isomorphism, there is just one projective plane of order 2. (Def. A proj. plane of order n is a set S of n^2+n+1 points having a collection (denoted Lns) of n^2+n+1 specified subsets of size n+1 called "lines", such that a) any two points lie in a unique line, and b) any two lines intersect in a unique point.) Given a proj. plane (S;Lns) of order 2, then #(S) = 7. Pick any point p, and note that there must be exactly 3 lines containing p. WLOG we denote these lines as {p,a2,a3}, {p,b2,b3}, {p,c2,c3}, where these 6 new elements must all be distinct. WLOG we may assume the line determined by {a2,b2} is {a2,b2,c2}. The remaining 3 lines are now completely determined as {a2,b3,c3},{a3,b2,c3} and {a3,b3,c2}. --Dan