2 problems

Let $K$ be one of the complexes described by Brehm and Kühnel: a triangulation of an $8$-manifold different from the sphere on $15$ vertices. Brehm–Kühnel's conjecture. These compl…

Consider the $15$-vertex combinatorial triangulation whose automorphism group is the icosahedral group $A_5$ acting transitively on the vertices. Let $M$ be the underlying topologi…