In‐plane structure of single‐layer tissues
The standard classification of tissues is based on their structure and function and includes connective, muscle, nervous, epithelial, and mineralized tissues. Connective tissue consists of cells dispersed within an inanimate extracellular matrix, and it sculpts the organs. Many epithelial cells are prismatic in shape and their sides are functionally distinct. The apical side faces the environment or the lumen, that is, the cavity of a structure or an organ such as blood vessel or intestine. The geometry of a simple epithelial tissue can be approximated by a polygonal tiling of a plane. In some tilings, a certain type of regularity such as translational order or bond-orientational order can be mathematically defined and measured. Most tilings seen in epithelia are random, that is, not characterized by an obvious kind of spatial order. The basic topological constraint imposed on the tilings can be formulated through a relation that the vertices, edges, and faces of the tiling must fulfill.