An Evolutionary Structure of Convex Pentagons on a C² Complete Surface and a Creation Principle of some Weighted Dendrites of Order Three

We reveal some new evolutionary structures of convex pentagons on a $C^2$ surface in the three dimensional Euclidean Space which is hidden on the notion of plasticity of weighted convex pentagons and quadrilaterals. We prove a creation principle for a weighted dendrite of order 3 on a $C^2$ surface which is derived by decreasing the degree of plasticity of weighted convex pentagons from 2 to 1. The creation principle of weighted dendrites of order 3 characterize the process of creation of various leaf tree types on surfaces.