The understanding of oblique detonation dynamics has both inherent basic research value for highspeed compressible reacting flow and propulsion application in hypersonic aerospace systems. In this study, the oblique detonation structures formed by semi-infinite cones are investigated numerically by solving the unsteady, two-dimensional axisymmetric Euler equations with a one-step irreversible Arrhenius reaction model. The present simulation results show that a novel wave structure, featured by two distinct points where there is close-coupling between the shock and combustion front, is depicted when either the cone angle or incident Mach number is reduced. This structure is analyzed by examining the variation of the reaction length scale and comparing the flow field with that of planar, wedge-induced oblique detonations. Further simulations are performed to study the effects of chemical length scale and activation energy, which are both found to influence the formation of this novel structure. The initiation mechanism behind the conical shock is discussed to investigate the interplay between the effect of the Taylor-Maccoll flow, front curvature, and energy releases from the chemical reaction in conical oblique detonations. The observed flow fields are interpreted by means of the energetic limit as in the critical regime for initiation of detonation. Published by AIP Publishing.