Curvature and Frustration in Cellular Systems

A cellular structure is a compromise between best local packing and filling space without gaps or overlap. The fact that soap bubble froths or the human epidermis are and remain steadily disordered, demonstrates that this compromise is essential. Two alternative methods are presented: decurving progressively and at random a cellular structure initially ordered in curved space, or building up the structure layer by layer from an arbitrary seed cell, like a puzzle without boundary. There is a narrow range of structures sandwiched between the froth with lowest interfacial energy and that with highest orientational entropy.