Ill 



because in that way the greatest volume is attained with the 

 least surface area. What then is the form assumed by cells in 

 aggregates, as in tissues r* 



If four spheres are placed at equal intervals about a central 

 one, so that the centers of all of them are in the same plane, 

 and then one is placed directly above and one directly below 

 the central one, there will be six surrounding the central one. 

 If now equal pressure is applied to all the surrounding spheres 

 the central one will assume the form of a cube. The familiar 

 "cannonball" stacking of spheres, with six surrounding a 

 central one, all with their centers in one plane, and then three 

 above and three below, gives rise to the rhombic dodecahedron. 

 The cube does not give economy of space per unit of volume; 

 and the rhombic dodecahedron is objectionable because of its 

 tetrahedral angles. Kelvin, having studied the investigations of 

 Plateau, on soap films, decided that tetrahedral angles were 

 unstable. To overcome this objection he described a fourteen- 

 sided figure, six surfaces of which are quadrilateral and eight 

 hexagonal; this he called a tetrakaidecahedron. If all the 

 quadrilaterals are squares and all the hexagons regular hexagons, 

 and the sides of the squares and hexagons all equal, the figure 

 is an "orthic tetrakaidecahedron." 



The recent investigations of Lewis show that the economy of 

 surface per unit of volume is greater for the tetrakaidecahedron 

 than for the rhombic dodecahedron. 



Lewis, studying cells of elder pith, found that the average 

 number of surfaces for one hundred cells was 13.96; and the 

 average for one hundred cells of human adipose tissue was 14.01, 

 suggesting very strikingly that cells in undifferentiated tissue 

 tend to be tetrakaidecahedra. 



Recent criticisms of this work, stating that orthic tetra- 

 kaidecahedra will not fill space when stacked together, can be 

 answered first, by demonstrating geometrically that these 

 figures will fill space — and this has been done — and secondly 

 by making models and stacking them together. 



The space-lattice concept, developed by crystallographers, 

 can be extended to tissues and tissue systems. If cells are 

 represented by a point or points, as for instance the center of 

 gravity of each cell, or a similar point on each surface of the 

 cell wall, a pattern of points is revealed, similar in many respects 



