The relation of the critical and neutral thicknesses and heat transfer characteristics for an insulated regular polygonal pipe are investigated by using a new wedge thermal resistance model based on its varying pipe surface area. It is found that the dimensionless heat transfer characteristics of the insulated polygonal pipes are the same as those of an insulated circular pipe. It is also found that the conventional constant surface area plate model cannot be used to analyse the insulated regular polygonal pipes, especially at the situations of small to medium pipe sizes and/or with a greater insulation thickness.