Hatcher, Algebraic Topology, Chapter 2, Section 1
28. Let be the cone of the 1-skeleton of , the union of all line segments joining the points in the six edges of to the barycenter of . Compute the local homology groups for all . Define to be the subspace of points such that for all , and compute the local homology groups . Use these calculations to determine which subsets have the property that for all homeomorphisms .