B. Hanson et J. Heinonen, An n-dimensional space that admits a Poincare inequality but has no manifold points, P AM MATH S, 128(11), 2000, pp. 3379-3390
For each integer n greater than or equal to 2 we construct a compact, geode
sic metric space X which has topological dimension n, is Ahlfors n-regular,
satisfies the Poincare inequality, possesses R-n as a unique tangent cone
at H-n almost every point, but has no manifold points.