A novel calss of subdivision schemes based on the hexagonal meshes is presented.It is called honeycomb subdivision which enlarges the field of subdivision surfaces. By introducing the concept of central control vertices into the schemes, the honeycomb subdivision has the advantages of flexible coefficients selection,easy control of shape,less complexity of large meshes, and applicability.Its properties are analyzed and appropriate subdivision rules are given to obtain limit surfaces with tangent continuity. It can interpolate the given control vertices under certain conditions.The schemes are applicable for shape modeling in computer animation and industrial prototype design.