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A minimal triangulation of the quaternionic projective plane

The problem of finding minimal triangulations of manifolds with respect to the number of vertices is a classical problem in combinatorial topology. We will always consider a triangulation to be simplicial, that is, the intersection of any two simplices is either empty or is a facet of both simplices. The solution of this problem is known for a fairly small set of manifolds. The difficulty of the problem increases especially with the growth of the dimension. In higher dimensions no examples of triangulations for most manifolds are known. In particular, finding a simple triangulation of a smooth manifold is of interest also from the point of view of possible discretisation of structures in differential topology (cf. [1]). A good survey on minimal triangulations can be found in [2] by Lutz. A combinatorial manifold is a simplicial complex such that the link of each vertex is piecewise linearly homeomorphic to the boundary of the simplex.