The octonionic projective plane

As mathematicians found out in the last century, there are only four normed division algebras1 over ℝ: real numbers themselves, complex numbers, quaternions and octonions. Whereas very well-known most of their properties carry to (apart from fact that these not commutative), octonions different harder handle since they even associative. However, can be used for several interesting topological constructions, often paralleling constructions known ℝ, ℂ or ℍ.