A theoretical study has predicted the course of chronoamperometry following the imposition of a large potential step on an electrode in the shape of an infinite cone, under the usual diffusion-controlled conditions (with diffusivity D). We show how the current density (at a distance r from the apex and at a time r after the step) depends on r(2)/Dt and on the semi-apical angle of the cone. The long-time version of this relationship predicts that a cone with a semi-apical angle of 54.74 degrees will display the unique voltammetric property of independence from D. The short-time relationship throws light on the voltammetric behaviour of vertices in general.