2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/168242We show that a weighted homogeneous complex surface singularity is metrically conical (i.e., bi-Lipschitz equivalent to a metric cone) only if its two lowest weights are equal. We also give an example of a pair of weighted homogeneous complex surface singularities that are topologically equivalent but not bi-Lipschitz equivalent.5 pages. Added result that nonhomogeneous cyclic quotients are not conicalAlgebraic GeometryGeometric TopologyMetric Geometry14B05, 32S50text