Triangulated Manifolds with Few Vertices: Vertex-Transitive   Triangulations I
  We describe an algorithm for the enumeration of (candidates of) vertex-transitive combinatorial $d$-manifolds. With an implementation of our algorithm, we determine, up to combinatorial equivalence, all combinatorial manifolds with a vertex-transitive automorphism group on $n\leq 13$ vertices. With the exception of actions of groups of small order, the enumeration is extended to 14 and 15 vertices. 
Ekkehard G. K\"ohler and Frank H. Lutz