vn] OF THE TETRAKAIDEKAHEDRON 553 



struction and otherwise, and has succeeded in shewing that the 

 tetrakaidekahedral form is closely approached, or even attained, in 

 certain simple and homogeneous tissues. After reconstructing a 

 large model of the cells of elder-pith, he finds that the fourteen-sided 

 figure clearly manifests itself as the characteristic or typical form 

 to which the cells approximate, in spite of repeated cell-divisions 

 and consequent inequalities of size. Counting in a hundred cells 

 the number of contacts which each made with its neighbours, that 

 is to say the total number both of actual and potential facets, Lewis 

 found that 74 per cent, of the cells were either 12, 13, 14, 15 or 

 16-sided, 56 per cent, either 13, 14 or 15-sided, and that the averagje 



-•-^ 



Fig. 214. Reconstructed models of cells of elder-pith, shewing a certain 

 approximation to 14-hedral form. From F. T. Lewis. 



number of facets or contacts was, in this instance, just 13-96. These 

 figures indicate the general symmetry of the cells, their departure 

 from the dodecahedral, and their tendency towards the tetra- 

 kaidekahedral, form*. 



But after all, the geometry of the 14-hedron, displayed to per- 

 fection by our soap-films in the twinkhng of an eye, is only roughly 

 developed in an organic structure, even one so delicate as elder- 

 pith; the conditions are no longer simple, for friction, viscosity and 



* F. T. Lewis, The typical shape of polyhedral cells in vegetable parenchyma, 

 and the restoration of that shape following cell-division, Proc. Amer. Acad, of Arts 

 and Sci. lviii, pp. 537-552, 1923, and other papers. See also {int. al.) J. W. Marvin, 

 The aggregation of orthis-tetrakaidekahedra. Science, lxxxiii, p. 188, 1936; 

 E. B. Metzger, An analysis of the orthotetrakaidekahedron, Bull. Torrey Bot. Club, 

 Liv, pp. 341-348, 1927. Professor van Iterson of Delft tells me that Asparagus 

 Sprengeri (a common greenhouse plant) is a good subject for shewing the 14-hedral 

 cells. 



