12 THE MOLECULAR ARCHITECTURE OF PLANT CELL WALLS 



considerable detail later on as one example of the control of cell shape 



by wall architecture. When, however, the original single cell develops, 



by continued division, into a mass of cells which adhere — that is 



immediately a tissue is formed — then it is understandable that the 



original spherical shape is lost. The shape which will then be taken up 



in a homogeneous tissue can be determined in any of three ways. If the 



tissue is truly homogeneous, i.e. if the cells are all of the same shape 



and size, then the problem resolves itself into the mathematical one of 



deciding which polyhedra are capable of filling space completely when 



placed regularly side by side, followed by the subsequent determination 



of the most probable of the forms which may thus be revealed. Secondly, 



argument can be made by analogy from inanimate bodies which appear 



to be developed under the same geometrical conditions, e.g. from the 



froth on soap solutions or even on beer. Here the bubbles which 



constitute the froth would be truly spherical, if free, and depart from 



this ideal shape only on account of the presence of neighbouring 



bubbles. Equally, the compression of closely packed spheres of plasticine 



or lead shot — even of swelling pea seeds — would yield polyhedra of the 



type required; finally, and perhaps most unequivocally, it is possible, 



under certain circumstances, to separate the cells in a homogeneous 



tissue and observe them from various directions under a microscope. 



This last type of observation, which might perhaps be expected to give 



the readiest answer, is in point of fact by no means so easy as it appears. 



All three methods have, however, been used and, in spite of a good deal 



of controversy in the past, there is at the moment a mutual agreement 



most unusual in the biological field. It seems 



now to be generally agreed that the shapes of 



all cells are based on the orthic tetrakaide- 



cahedron or cubo-octahedron almost in the 



form, therefore, suggested by Kieser more than 



100 years ago. This was originally suggested by 



Lord Kelvin as very nearly the form soap 



bubbles assume when filling space completely 



Fig. 1. Diagrammatic ^^^ jg shown in Fig. 1. There is, however, one 



representation of th^ ,., ,.„ . ° ^ ,. ,. 



ideal shape of meristem^ slight modification to be made in this conven- 



atic cells. The polyhe- tional figure in that the eight hexagonal faces 

 dron has eight hexagonal , , , . , , . . • 



and six tetragonal faces, are not plane but are slightly curved producing 



the so-called "body of Thomson". This has 



also been reported to be the case in plant cells (1). 



It is not, of course, to be assumed for a moment that all the cells in a 



naturally occurring tissue will adopt this ideal shape. The mere fact of 



